Deck 10: Statistical Inferences About Two Populations

Question 1

In a set of matched samples, each data value in one sample is related to or matched with a corresponding data value in the other sample.

Answer 1

True

Question 2

An appropriate sampling plan to determine if there is a difference in the speed of a wireless router from two different manufacturers, consists of a network manager drawing independent samples of wireless routers from the two manufacturers and comparing the difference in the sample means for the connection speed.

Answer 2

True

Question 3

If a 98% confidence interval for the difference in the two population means does not contain zero, then the null hypothesis of a zero difference between the two population means cannot be rejected at a 0.02 level of significance.

Answer 3

False

Question 4

Hypothesis tests conducted on sets of matched samples are sometimes referred to as correlated t tests.

Question 5

In order to construct an interval estimate of the difference in the means of two normally distributed populations with unknown but equal variances, using two independent samples of size n₁ and n₂, we must use a t distribution with (n₁ + n₂ − 2)degrees of freedom.

Question 6

If the sample sizes are small, but the populations are normally distributed and the population variances are known, the z-statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

Question 7

When finding a confidence interval for the difference between two population proportions we use a pooled estimate of the proportion.

Question 8

If a 90% confidence interval for the difference in the two population means contains zero, then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.

Question 9

If the populations are normally distributed and the variances of the two populations are equal, it is appropriate to use the "pooled" formula to determine the t-statistic for the hypothesis test of the difference in the two population means.

Question 10

If the populations are normally distributed but the population variances are unknown the t-statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

Question 11

If the populations are normally distributed and the variances of the two populations are not equal, it is appropriate to use the "unpooled" formula to determine the t-statistic for the hypothesis test of the difference in the two population means.

Question 12

The difference in two sample means is normally distributed for sample sizes ≥ 30, only if the populations are normally distributed.

Question 13

Sets of matched samples are also referred to as dependent samples.

Question 14

If the populations are normally distributed but the population variances are unknown the z-statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

Question 15

In conducting a matched-pairs hypothesis test, the null and alternative hypotheses always represent one-tailed tests.

Question 16

In order to construct an interval estimate of the difference in the means of two normally distributed populations with unknown but equal variances, using two independent samples of size n₁ and n₂, we must use a t distribution with (n₁ + n₂ -1)degrees of freedom.

Question 17

If the sample sizes are greater than 30 and the population variances are known, the basis for statistical inferences about the difference in two population means using two independent random samples is the z-statistic, regardless of the shapes of the population distributions.

Question 18

Testing the difference in two population proportions is useful whenever the researcher is interested in comparing the proportion of one population that has certain characteristic with the proportion of the second population that has the same characteristic.

Question 19

When testing for the difference between two population proportions we use a pooled estimate of the proportion.

Question 20

If the variances of the two populations are not equal, it is appropriate to use the "pooled" formula to determine the t-statistic for the hypothesis test of the difference in the two population means.

Question 21

A researcher wishes to determine the difference in two population means.To do this, she randomly samples 9 items from each population and computes a 90% confidence interval.The sample from the first population produces a mean of 780 with a standard deviation of 240.The sample from the second population produces a mean of 890 with a standard deviation of 280.Assume that the values are normally distributed in each population.The point estimate for the difference in the means of these two populations is _______.

A)-110
B)40
C)-40
D)0
E)240

Question 22

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1)and 60 Minutes (population 2).Previous studies indicate no difference in the ages of the two audiences.(The mean age of each audience is the same.)Lucy plans to test this hypothesis using a random sample of 100 from each audience.Her alternate hypothesis is ____________.

A) $\mu$ ₁ - $\mu$ ₂ ≤ 0
B) $\mu$ ₁ - $\mu$ ₂ ≥ 0
C) $\mu$ ₁ - $\mu$ ₂ = 0
D) $\mu$ ₁ - $\mu$ ₂ $\neq$ 0
E) $\mu$ ₁ - $\mu$ ₂ = 1

Question 23

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course.He wants to prove that Palmetto Dunes residents (population 1)play golf more often than Ocean Greens residents (population 2).Roberto commissions a market survey to test this hypothesis.The market researcher used a random sample of 64 individuals from each suburb, and reported the following: $\bar { x }$ ₁ = 15 times per month and $\bar { x }$ ₂ = 14 times per month.Assume that $\sigma$ ₁ = 2 and $\sigma$ ₂ = 3.With $\alpha$ = .01, the critical z value is _________________.

A)-1.96
B)1.96
C)-2.33
D)-1.33
E)2.33

Question 24

A researcher is interested in testing to determine if the mean price of a casual lunch is different in the city than it is in the suburbs.The null hypothesis is that there is no difference in the population means (i.e.the difference is zero).The alternative hypothesis is that there is a difference (i.e.the difference is not equal to zero).He randomly selects a sample of 9 lunch tickets from the city population resulting in a mean of $14.30 and a standard deviation of $3.40.He randomly selects a sample of 14 lunch tickets from the suburban population resulting in a mean of $11.80 and a standard deviation $2.90.He is using an alpha value of .10 to conduct this test.Assuming that the populations are normally distributed, the critical t value from the table is _______.

A)1.323
B)1.721
C)1.717 This is the value for 22 df (a wrong answer, but a detractor and corrected).
D)1.321
E)2.321

Question 25

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1)and 60 Minutes (population 2).Previous studies indicate no difference in the ages of the two audiences.(The mean age of each audience is the same.)Her staff randomly selected 100 people from each audience, and reported the following: $\bar { x }$ ₁ = 43 years and $\bar { x }$ ₂ = 45 years.Assume that $\sigma$ ₁ = 5 and $\sigma$ ₂ = 8.With a two-tail test and $\alpha$ = .05, the appropriate decision is _________________.

A)do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
B)reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ > 0
C)reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
D)do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ < 0
E)do nothing

Question 26

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1)and 60 Minutes (population 2).Previous studies indicate no difference in the ages of the two audiences.(The mean age of each audience is the same.)Her staff randomly selected 100 people from each audience, and reported the following: $\bar { x }$ ₁ = 43 years and $\bar { x }$ ₂ = 45 years.Assume that $\sigma$ ₁ = 5 and $\sigma$ ₂ = 8.With a two-tail test and $\alpha$ = .05, the critical z values are _________________.

A)-1.64 and 1.64
B)-1.96 and 1.96
C)-2.33 and 2.33
D)-2.58 and 2.58
E)-2.97 and 2.97

Question 27

The F statistic is a ratio of two independent sample variances.

Question 28

To test hypotheses about the equality of two population variances, the ratio of the variances of the samples from the two populations is tested using the F test.

Question 29

A researcher wants to estimate the difference in the means of two populations.A random sample of 36 items from the first population results in a sample mean of 430.A random sample of 49 items from the second population results in a sample mean of 460.The population standard deviations are 120 for the first population and 140 for the second population.From this information, a 95% confidence interval for the difference in population means is _______.

A)-95.90 to 35.90
B)-85.44, 25.44
C)-76.53 to 16.53
D)-102.83 to 42.43
E)98.45 to 125.48

Question 30

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course.He wants to prove that Palmetto Dunes residents (population 1)play golf more often than Ocean Greens residents (population 2).Roberto commissions a market survey to test this hypothesis.The market researcher used a random sample of 64 individuals from each suburb, and reported the following: $\bar { x }$ ₁ = 15 times per month and $\bar { x }$ ₂ = 14 times per month.Assume that $\sigma$ ₁ = 2 and $\sigma$ ₂ = 3.With $\alpha$ = .01, the appropriate decision is _________________.

A)reject the null hypothesis $\sigma$ ₁² < $\sigma$ ₂²
B)accept the alternate hypothesis $\mu$ ₁- $\mu$ ₂ $\gt$ 0
C)reject the alternate hypothesis n₁ = n₂ = 64
D)fail to reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
E)do nothing

Question 31

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course.He wants to prove that Palmetto Dunes residents (population 1)play golf more often than Ocean Greens residents (population 2).Roberto commissions a market survey to test this hypothesis.The market researcher used a random sample of 64 individuals from each suburb, and reported the following: $\bar { x }$ ₁ = 15 times per month and $\bar { x }$ ₂ = 14 times per month.Assume that $\sigma$ ₁ = 2 and $\sigma$ ₂ = 3.With $\alpha$ = .01, the observed z value is _________________.

A)2.22
B)12.81
C)4.92
D)3.58
E)1.96

Question 32

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course.He wants to prove that Palmetto Dunes residents (population 1)play golf more often than Ocean Greens residents (population 2).Roberto commissions a market survey to test this hypothesis.The market researcher used a random sample of 64 individuals from each suburb, and reported the following: $\bar { x }$ ₁ = 16 times per month and $\bar { x }$ ₂ = 14 times per month.Assume that $\sigma$ ₁ = 4 and $\sigma$ ₂ = 3.With $\alpha$ = .01, the observed z value is _________________.

A)18.29
B)6.05
C)5.12
D)3.40
E)3.20

Question 33

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1)and 60 Minutes (population 2).Previous studies indicate no difference in the ages of the two audiences.(The mean age of each audience is the same.)Her staff randomly selected 100 people from each audience, and reported the following: $\bar { x }$ ₁ = 43 years and $\bar { x }$ ₂ = 45 years.Assume that $\sigma$ ₁ = 5 and $\sigma$ ₂ = 8.Assuming a two-tail test and $\alpha$ = .05, the observed z value is _________________.

A)-2.12
B)-2.25
C)-5.58
D)-15.38
E)-20.68

Question 34

A researcher is interested in testing to determine if the mean price of a casual lunch is different in the city than it is in the suburbs.The null hypothesis is that there is no difference in the population means (i.e.the difference is zero).The alternative hypothesis is that there is a difference (i.e.the difference is not equal to zero).He randomly selects a sample of 9 lunch tickets from the city population resulting in a mean of $14.30 and a standard deviation of $3.40.He randomly selects a sample of 14 lunch tickets from the suburban population resulting in a mean of $11.80 and a standard deviation $2.90.He is using an alpha value of .10 to conduct this test.Assuming that the populations are normally distributed and that the population variances are approximately equal, the degrees of freedom for this problem are _______.

A)23
B)22
C)21
D)1
E)2

Question 35

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course.He wants to prove that Palmetto Dunes residents (population 1)play golf more often than Ocean Greens residents (population 2).Roberto plans to test this hypothesis using a random sample of 81 individuals from each suburb.His null hypothesis is __________.

A) $\sigma$ ₁² < $\sigma$ ₂²
B) $\mu$ ₁- $\mu$ ₂ $\gt$ 0
C)p₁ - p₂ = 0
D) $\mu$ ₁ - $\mu$ _{2 ≤} 0 I thought it less confusingfor students to be consistent with the text.I have seen other textbooks also use only the = for the null hypothesis as that is the critical element.
The less than or equal to is technically correct.The book shows it as an = sign, which is not correct when describing the null hypothesis for this one-tailed test.
E)s₁ - s₂ = 0

Question 36

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1)and 60 Minutes (population 2).Previous studies indicate no difference in the ages of the two audiences.(The mean age of each audience is the same.)Lucy plans to test this hypothesis using a random sample of 100 from each audience.Her null hypothesis is ____________.

A) $\mu$ ₁ - $\mu$ ₂ $\neq$ 0
B) $\mu$ ₁ - $\mu$ ₂ ≥ 0
C) $\mu$ ₁ - $\mu$ ₂ = 0
D) $\mu$ ₁ - $\mu$ ₂ ≤ 0
E) $\mu$ ₁ - $\mu$ ₂ ≤ 1

Question 37

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course.He wants to prove that Palmetto Dunes residents (population 1)play golf more often than Ocean Greens residents (population 2).Roberto commissions a market survey to test this hypothesis.The market researcher used a random sample of individuals from each suburb, and reported the following: $\bar { x }$ ₁ = 16 times per month and $\bar { x }$ ₂ = 14 times per month.Assume that $\sigma$ ₁ = 4 and $\sigma$ ₂ = 3.With $\alpha$ = .01, the appropriate decision is _____________.

A)do nothing
B)reject the null hypothesis $\mu$ ₁ < $\mu$ ₂
C)accept the alternate hypothesis $\mu$ ₁- $\mu$ ₂ $\gt$ 0
D)reject the alternate hypothesis n₁ = n₂ = 64
E)do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0

Question 38

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course.He wants to prove that Palmetto Dunes residents (population 1)play golf more often than Ocean Greens residents (population 2).Roberto plans to test this hypothesis using a random sample of 81 individuals from each suburb.His alternative hypothesis is __________.

A) $\sigma$ ₁² < $\sigma$ ₂²
B) $\mu$ ₁- $\mu$ ₂ $\gt$ 0
C)p₁ - p₂ = 0
D) $\mu$ ₁ - $\mu$ ₂ = 0
E)s₁ - s₂ > 0

Question 39

The F test of two population variances is extremely robust to the violations of the assumption that the populations are normally distributed.

Question 40

The ratio of two independent sample variances follows the F distribution.

Question 41

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses.Her goal is 100% of orders shipped within 24 hours.In previous years, neither warehouse has achieved the goal, but the West Coast Warehouse has consistently out-performed the East Coast Warehouse.Her staff randomly selected 200 orders from the West Coast Warehouse (population 1)and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours.Assuming $\alpha$ = 0.05, the critical z value is ___________________.

A)-1.96
B)-1.64
C)1.64
D)1.96
E)2.33

Question 42

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses.Her goal is 100% of orders shipped within 24 hours.In previous years, neither warehouse has achieved the goal, but the West Coast Warehouse has consistently out-performed the East Coast Warehouse.Her staff randomly selected 200 orders from the West Coast Warehouse (population 1)and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours.Assuming $\alpha$ = 0.05, the appropriate decision is ___________________.

A)do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
B)do not reject the null hypothesis p₁ - p₂ = 0
C)reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
D)reject the null hypothesis p₁ - p₂ = 0
E)do not reject the null hypothesis p₁ - p₂ ≥ 0

Question 43

A researcher believes a new diet should improve weight gain.To test his hypothesis a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected.The selected people on the old diet gain an average of 5 pounds with a standard deviation of 2 pounds, while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds.Assume that the values are normally distributed in each population and that the population variances are approximately equal.Using $\alpha$ = 0.05, the observed t value for this test is _______.

A)-1.96
B)-1.645
C)-2.100
D)-3.79
E)-1.734

Question 44

A researcher wants to conduct a before/after study on 11 subjects to determine if a new cholesterol medication results in higher HDL cholesterol readings.The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is not zero.Scores are obtained on the subjects both before and after taking the medication.After subtracting the after scores from the before scores, the average difference is computed to be -2.40 with a sample standard deviation of 1.21.Assume that the differences are normally distributed in the population.The observed t value for this test is _______.

A)-21.82
B)-6.58
C)-2.4
D)1.98
E)2.33

Question 45

A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: $$\begin{array} { | c | c | c | } \hline \text { Pair } & \text { Group 1 } & \text { Group 2 } \\\hline 1 & 10 & 12 \\\hline 2 & 8 & 9 \\\hline 3 & 11 & 11 \\\hline 4 & 8 & 10 \\\hline 5 & 9 & 12 \\\hline\end{array}$$ Assume that the data are normally distributed in the population.The level of significance is selected to be 0.10.If a two-tailed test is performed, the null hypothesis would be rejected if the observed value of t is _______.

A)less than -1.533 or greater than 1.533
B)less than -2.132 or greater than 2.132
C)less than -2.776 or greater than 2.776
D)less than -1.860 or greater than 1.860
E)less than -2.000 or greater than 2.000

Question 46

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses.Her goal is 100% of orders shipped within 24 hours.In previous years, neither warehouse has achieved the goal, but the West Coast Warehouse has consistently out-performed the East Coast Warehouse.Her staff randomly selected 200 orders from the West Coast Warehouse (population 1)and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours.Assuming $\alpha$ = 0.05, the observed z value is ___________________.

A)-3.15
B)2.42
C)1.53
D)0.95
E)1.08

Question 47

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses.Her goal is 100% of orders shipped within 24 hours.In previous years, neither warehouse has achieved the goal, but the West Coast Warehouse has consistently out-performed the East Coast Warehouse.Her staff randomly selected 200 orders from the West Coast Warehouse (population 1)and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 356 orders within 24 hours.Assuming $\alpha$ = 0.05, the observed z value is ___________________.

A)-3.15
B)2.42
C)1.53
D)0.95
E)1.05

Question 48

A researcher wishes to determine the difference in two population means.To do this, she randomly samples 9 items from each population and computes a 90% confidence interval.The sample from the first population produces a mean of 780 with a standard deviation of 240.The sample from the second population produces a mean of 890 with a standard deviation of 280.Assume that the values are normally distributed in each population and that the population variances are approximately equal.The critical t value used from the table for this is _______.

A)1.860
B)1.734
C)1.746
D)1.337
E)2.342

Question 49

A researcher is estimating the average difference between two population means based on matched-pairs samples.She gathers data on each pair in the study resulting in: $$\begin{array} { | r | r | r | } \hline {\text { Pair } } & \text { Group 1 } & \text { Group } 2 \\\hline 1 & 10 & 12 \\\hline 2 & 8 & 9 \\\hline 3 & 11 & 11 \\\hline 4 & 8 & 10 \\\hline 5 & 9 & 12 \\\hline\end{array}$$ Assume that the data are normally distributed in the population.A 95% confidence interval would be _______.

A)-3.02 to -0.18
B)-1.6 to -1.09
C)-2.11 to 1.09
D)-2.11 to -1.09
E)-3.23 to 2.23

Question 50

A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: $$\begin{array} { | c | c | c | } \hline \text { Pair } & \text { Group 1 } & \text { Group } 2 \\\hline 1 & 10 & 12 \\\hline 2 & 8 & 9 \\\hline 3 & 11 & 11 \\\hline 4 & 8 & 10 \\\hline 5 & 9 & 12 \\\hline\end{array}$$ Assume that the data are normally distributed in the population.The sample standard deviation (s_d)of the differences is _______.

A)1.30
B)1.14
C)1.04
D)1.02
E)1.47

Question 51

A researcher wants to conduct a before/after study on 11 subjects to determine if a new cholesterol medication results in higher HDL cholesterol readings.The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is not zero.Scores are obtained on the subjects both before and after taking the medication.After subtracting the after scores from the before scores, the average difference is computed to be -2.40 with a sample standard deviation of 1.21.Assume that the differences are normally distributed in the population.The degrees of freedom for this test are _______.

A)11
B)10
C)9
D)20
E)2

Question 52

A researcher is estimating the average difference between two population means based on matched-pairs samples.She gathers data on each pair in the study resulting in: $$\begin{array} { | r | r | r | } \hline \text { Pair } & \text { Group 1 } & \text { Group } 2 \\\hline 1 & 10 & 12 \\\hline 2 & 8 & 9 \\\hline 3 & 11 & 11 \\\hline 4 & 8 & 10 \\\hline 5 & 9 & 12 \\\hline\end{array}$$ Assume that the data are normally distributed in the population.To obtain a 95% confidence interval, the table t value would be _______.

A)2.132
B)1.86
C)2.306
D)2.976
E)2.776

Question 53

A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: $$\begin{array} { | c | c | c | } \hline \text { Pair } & \text { Group 1 } & \text { Group 2 } \\\hline 1 & 10 & 12 \\\hline 2 & 8 & 9 \\\hline 3 & 11 & 11 \\\hline 4 & 8 & 10 \\\hline 5 & 9 & 12 \\\hline\end{array}$$ Assume that the data are normally distributed in the population.The degrees of freedom in this problem are _______.

A)4
B)8
C)5
D)9
E)3

Question 54

A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: $$\begin{array} { | c | c | c | } \hline \text { Pair } & \text { Group 1 } & \text { Group 2 } \\\hline 1 & 10 & 12 \\\hline 2 & 8 & 9 \\\hline 3 & 11 & 11 \\\hline 4 & 8 & 10 \\\hline 5 & 9 & 12 \\\hline\end{array}$$ Assume that the data are normally distributed in the population.The level of significance is selected to be 0.10.If the alternative hypothesis is that the average difference is greater than zero, the null hypothesis would be rejected if the observed value of t is _______.

A)greater than 1.533
B)less than -1.533
C)greater than 2.132
D)less than -2.132
E)equal to 2.333

Question 55

A researcher wants to conduct a before/after study on 11 subjects to determine if a new cholesterol medication results in higher HDL cholesterol readings.The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is not zero.Scores are obtained on the subjects both before and after taking the medication.After subtracting the after scores from the before scores, the average difference is computed to be -2.40 with a sample standard deviation of 1.21.A 0.05 level of significance is selected.Assume that the differences are normally distributed in the population.The table t value for this test is _______.

A)1.812
B)2.228
C)2.086
D)2.262
E)3.2467

Question 56

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses.Her goal is 100% of orders shipped within 24 hours.In previous years, neither warehouse has achieved the goal, but the West Coast Warehouse has consistently out-performed the East Coast Warehouse.Her staff randomly selected 200 orders from the West Coast Warehouse (population 1)and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours.Maureen's alternative hypothesis is _______.

A)p₁ - p₂ $\neq$ 0
B) $\mu$ ₁ - $\mu$ ₂ > 0
C)p₁ - p₂ > 0
D) $\mu$ ₁ - $\mu$ ₂ $\neq$ 0
E) $\mu$ ₁ - $\mu$ ₂ ≥ 0

Question 57

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses.Her goal is 100% of orders shipped within 24 hours.In previous years, neither warehouse has achieved the goal, but the West Coast Warehouse has consistently out-performed the East Coast Warehouse.Her staff randomly selected 200 orders from the West Coast Warehouse (population 1)and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 356 orders within 24 hours.Assuming $\alpha$ = 0.05, the appropriate decision is ___________________.

A)reject the null hypothesis p₁ - p₂ = 0
B)reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ ≤ 0
C)do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
D)do not reject the null hypothesis p₁ - p₂ = 0
E)do not reject the null hypothesis p₁ - p₂ ≥ 0

Question 58

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses.Her goal is 100% of orders shipped within 24 hours.In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse.Her staff randomly selected 200 orders from the West Coast Warehouse (population 1)and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours.Maureen's null hypothesis is ____.

A)p₁ - p₂ = 0
B) $\mu$ ₁ - $\mu$ ₂ = 0
C)p₁ - p₂ ≥ 0
D) $\mu$ ₁ - $\mu$ ₂ ≤ 0
E) $\mu$ ₁ - $\mu$ ₂ ≥ 0

Question 59

A researcher is estimating the average difference between two population means based on matched-pairs samples.She gathers data on each pair in the study resulting in: $$\begin{array} { | l | l | l | } \hline \text { Pair } & \text { Group 1 } & \text { Group 2 } \\\hline 1 & 10 & 12 \\\hline 2 & 8 & 9 \\\hline 3 & 11 & 11 \\\hline 4 & 8 & 10 \\\hline 5 & 9 & 12 \\\hline\end{array}$$ Assume that the data are normally distributed in the population.To obtain a 90% confidence interval, the table t value would be _______.

A)1.86
B)1.397
C)1.533
D)2.132
E)3.346

Question 60

A researcher believes a new diet should improve weight gain.To test his hypothesis a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected.The selected people on the old diet gain an average of 5 pounds with a standard deviation of 2 pounds, while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds.Assume that the values are normally distributed in each population and that the population variances are approximately equal.Using $\alpha$ = 0.05, the critical t value used from the table for this is _______.

A)-1.96
B)-1.645
C)-2.100
D)-3.79
E)-1.734

Question 61

Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks.Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index.Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise.Her staff reported that during the last nine quarters, the price variance for the S&P 500 index (population 1)was 25, and for the last seven quarters, the price variance for XYC common (population 2)was 8.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05, Tamara's alternate hypothesis is _______.

A) $\sigma$ ₁ ²= $\sigma$ ₂ ²
B) $\sigma$ ₁ ² $\neq$$\sigma$ ₂ ²
C) $\sigma$ ₁ ² $\ge$$\sigma$ ₂ ²
D) $\sigma$ ₁ ² $\lt$$\sigma$ ₂ ²
E)s ₁ ² $\lt$ ₂ ²

Question 62

Suppose that .06 of each of two populations possess a given characteristic.Samples of size 400 are randomly drawn from each population.What is the probability that the differences in sample proportions will be greater than 0.02?

A)0.4535
B)0.9535
C)0.1170
D)0.5465
E)0.4650

Question 63

A university administrator believes that business students are more likely to be working and going to school than their liberal arts majors.This information may lead to the business school offering courses in the evening hours while the liberal arts college maintains a daytime schedule.To test this theory, the proportion of business students who are working at least 20 hours per week is compared to the proportion of liberal arts students who are working at least 20 hours per week.A random sample of 600 from the business school has been taken and it is determined that 480 students work at least 20 hours per week.A random sample of 700 liberal arts students showed that 350 work at least 20 hours per week.The observed z for this is _______.

A)0.300
B)0.624
C)0.638
D)11.22
E)13.42

Question 64

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc.(population 1), and switching to Stockton Steel (population 2), since Stockton's rods had less variability in length.Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes.The results for Redding were s₁² = 0.10 with n₁ = 8, and, for Stockton, the results were s₂² = 0.05 with n₂ = 10.Assume that rod lengths are normally distributed in the population.If $\alpha$ = 0.05, the observed F value is ___________.

A)0.50
B)2.00
C)1.41
D)0.91
E)0.71

Question 65

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc.(population 1), and switching to Stockton Steel (population 2), since Stockton's rods had less variability in length.Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes.The results for Redding were s₁² = 0.10 with n₁ = 8, and, for Stockton, the results were s₂² = 0.05 with n₂ = 10.Assume that rod lengths are normally distributed in the population If $\alpha$ = 0.05, the appropriate decision is ________.

A)reject the null hypothesis $\sigma$ ₁ ²= $\sigma$ ₁ ²
B)reject the null hypothesis $\sigma$ ₁ ² $\le$ $\sigma$ ₁ ²
C)do not reject the null hypothesis $\sigma$ ₁ ² $\le$$\sigma$ ₁ ²
D)do not reject the null hypothesis $\sigma$ ₁ ² $\lt$$\sigma$ ₁ ²
E)do nothing

Question 66

Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks.Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index.Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise.Her staff reported that during the last nine quarters, the price variance for the S&P 500 index (population 1)was 25, and for the last seven quarters, the price variance for XYC common (population 2)was 6.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05, the appropriate decision is _______.

A)reject the null hypothesis $\sigma$ ₁ ² ≤ $\sigma$ ₁ ²
B)reject the null hypothesis $\sigma$ ₁ ² $\neq$ $\sigma$ ₁ ²
C)do not reject the null hypothesis $\sigma$ ₁ ²= $\sigma$ ₁ ²
D)do not reject the null hypothesis $\sigma$ ₁ ² $\neq$$\sigma$ ₁ ²
E)maintain status quo

Question 67

Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks.Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index.Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise.Her staff reported that during the last nine quarters, the price variance for the S&P 500 index (population 1)was 25, and for the last seven quarters, the price variance for XYC common (population 2)was 8.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05, the observed F value is _______.

A)3.13
B)0.32
C)1.77
D)9.77
E)9.87

Question 68

Suppose that .06 of each of two populations possess a given characteristic.Samples of size 400 are randomly drawn from each population.The probability that the difference between the first sample proportion which possess the given characteristic and the second sample proportion which possess the given characteristic being more than +.03 is _______.

A)0.4943
B)0.9943
C)0.0367
D)0.5057
E)0.5700

Question 69

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc.(population 1), and switching to Stockton Steel (population 2), since Stockton's rods had less variability in length.Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes.The results for Redding were s₁² = 0.10 with n₁ = 8, and, for Stockton, the results were s₂² = 0.05 with n₂ = 10.Assume that rod lengths are normally distributed in the population.If $\alpha$ = 0.05, the critical F value is _____________.

A)3.68
B)3.29
C)3.50
D)3.79
E)3.99

Question 70

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc.(population 1), and switching to Stockton Steel (population 2), since Stockton's rods had less variability in length.Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes.The results for Redding were s₁² = 0.10 with n₁ = 8, and, for Stockton, the results were s₂² = 0.05 with n₂ = 10.Assume that rod lengths are normally distributed in the population.Claude's alternative hypothesis is _____________.

A) $\sigma$ ₁ ²= $\sigma$ ₂ ²
B) $\sigma$ ₁ ² $\neq$$\sigma$ ₂ ²
C) $\sigma$ ₁ ² $\gt$$\sigma$ ₂ ²
D) $\sigma$ ₁ ² $\lt$$\sigma$ ₂ ²
E)s ₁ ² $\lt$ s ₂ ²

Question 71

Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks.Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index.Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise.Her staff reported that during the last nine quarters, the price variance for the S&P 500 index (population 1)was 25, and for the last seven quarters, the price variance for XYC common (population 2)was 8.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05, the appropriate decision is _______.

A)reject the null hypothesis $\sigma$ ₁ ²= $\sigma$ ₁ ²
B)reject the null hypothesis $\sigma$ ₁ ² $\neq$$\sigma$ ₁ ²
C)do not reject the null hypothesis $\sigma$ ₁ ² $\le$ $\sigma$ ₂ ²
D)do not reject the null hypothesis $\sigma$ ₁ ² $\neq$ $\sigma$ ₁ ²
E)do nothing

Question 72

Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks.Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index.Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise.Her staff reported that during the last nine quarters, the price variance for the S&P 500 index (population 1)was 25, and for the last seven quarters, the price variance for XYC common (population 2)was 8.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05, Tamara's null hypothesis is _______.

A) $\sigma$ ₁ ² $\le$$\sigma$ ₂ ²
B) $\sigma$ ₁ ² $\neq$$\sigma$ ₂ ²
C) $\sigma$ ₁ ² $\gt$$\sigma$ ₂ ²
D) $\sigma$ ₁ ² $\lt$$\sigma$ ₂ ²
E)s ₁ ² $\lt$ s ₂ ²

Question 73

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc.(population 1), and switching to Stockton Steel (population 2), since Stockton's rods had less variability in length.Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes.The results for Redding were s₁² = 0.15 with n₁ = 8, and, for Stockton, the results were s₂² = 0.04 with n₂ = 10.Assume that rod lengths are normally distributed in the population If $\alpha$ = 0.05, the observed F value is ___________.

A)0.27
B)0.52
C)1.92
D)3.75
E)4.25

Question 74

Suppose that .06 of each of two populations possess a given characteristic.Samples of size 400 are randomly drawn from each population.The standard deviation for the sampling distribution of differences between the first sample proportion and the second sample proportion (used to calculate the z score)is _______.

A)0.00300
B)0.01679
C)0.05640
D)0.00014
E)0.12000

Question 75

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc.(population 1), and switching to Stockton Steel (population 2), since Stockton's rods had less variability in length.Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes.The results for Redding were s₁² = 0.10 with n₁ = 8, and, for Stockton, the results were s₂² = 0.05 with n₂ = 10.Assume that rod lengths are normally distributed in the population.Claude's null hypothesis is ________________.

A) $\sigma$ ₁ ² $\le$ $\sigma$ ₂ ²
B) $\sigma$ ₁ ² $\neq$$\sigma$ ₂ ²
C) $\sigma$ ₁ ² $\gt$ $\sigma$ ₂ ²
D) $\sigma$ ₁ ² $\lt$$\sigma$ ₂ ²
E)s ₁ ² $\lt$ s ₂ ²

Question 76

A random sample of 400 items from a population shows that 160 of the sample items possess a given characteristic.A random sample of 400 items from a second population resulted in 110 of the sample items possessing the characteristic.Using these data, a 99% confidence interval is constructed to estimate the difference in population proportions which possess the given characteristic.The resulting confidence interval is _______.

A)0.06 to 0.19
B)0.05 to 0.22
C)0.09 to 0.16
D)0.04 to 0.21
E)0.05 to 0.23

Question 77

A researcher is interested in estimating the difference in two population proportions.A sample of 400 from each population results in sample proportions of .61 and .64.The point estimate of the difference in the population proportions is _______.

A)-0.030
B)0.625
C)0.000
D)0.400
E)0.500

Question 78

A researcher is interested in estimating the difference in two population proportions.A sample of 400 from each population results in sample proportions of .61 and .64.A 90% confidence interval for the difference in the population proportions is _______.

A)-0.10 to 0.04
B)-0.09 to 0.03
C)-0.11 to 0.05
D)-0.07 to 0.01
E)-0.08 to 0.12

Question 79

Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks.Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index.Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise.Her staff reported that during the last nine quarters, the price variance for the S&P 500 index (population 1)was 25, and for the last seven quarters, the price variance for XYC common (population 2)was 6.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05, the observed F value is _______.

A)17.36
B)2.04
C)0.24
D)4.77
E)4.17

Question 80

Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks.Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index.Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise.Her staff reported that during the last nine quarters, the price variance for the S&P 500 index (population 1)was 25, and for the last seven quarters, the price variance for XYC common (population 2)was 8.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05, the critical F value is _______.

A)3.68
B)3.58
C)4.15
D)3.29
E)4.89