Deck 10: Statistical Inferences About Two Populations

Question 1

Test hypotheses and develop confidence intervals about the difference in two population proportions.

Answer 1

The population means are analyzed by comparing two sample means.When sample sizes are large (n ≥ 30)and population variances are known,a z test is used.When sample sizes are small,the population variances are known,and the populations are normally distributed,the z test is used to analyze the population means.If the population variances are unknown,and the populations are normally distributed,the t test of means for independent samples is used.For populations that are related on some measure,such as twins or before-and-after,a t test for dependent measures (matched pairs)is used.The difference in two population proportions can be tested or estimated using a z test.

Question 2

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

Answer 2

False

Question 3

In order to construct an interval estimate for 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.

Answer 3

True

Question 4

Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Question 5

In order to construct an interval estimate for 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)degrees of freedom.

Question 6

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 7

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

Question 8

To determine if there is a difference in the strength of steel produced from two different production processes,a process manager will draw independent samples from the two processes and compare the difference in the sample means.

Question 9

Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Question 10

Test hypotheses about the difference in two population variances using the F distribution.

Question 11

If 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 12

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.

Question 13

If 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 14

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 15

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 16

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 17

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 18

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

Question 19

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 20

Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Question 21

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

Question 22

A researcher wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores.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 the treatment.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 23

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 24

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: 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 25

Lucy Baker is analyzing demographic characteristics of two television programs,Lost (population 1)and Heroes (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 26

A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population.The sample standard deviation (s)is ___.

A)1.3
B)1.14
C)1.04
D)1.02
E)1.47

Question 27

A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: 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 28

A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: 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 29

A researcher is interested in testing to determine if the mean of population one is greater than the mean of population two.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 items from population one resulting in a mean of 14.3 and a standard deviation of 3.4.He randomly selects a sample of 14 items from population two resulting in a mean of 11.8 and a standard deviation 2.9.He is using an alpha value of .10 to conduct this test.Assuming that the populations are normally distributed,the degrees of freedom for this problem are ___.

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

Question 30

A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: 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 31

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

Question 32

Restaurateur Denny Valentine is evaluating two sites,Raymondville and Rosenberg,for his next restaurant.He wants to prove that Raymondville residents (population 1)dine out more often than Rosenberg residents (population 2).Denny plans to test this hypothesis using a random sample of 81 families from each suburb.His null hypothesis is ___.

A) $\sigma$ ₁² < $\sigma$ ₂²
B) $\mu$ ₁ - µ₂ > 0
C)p₁ - p₂ = 0
D) $\mu$ ₁ - $\mu$ ₂ = 0
E)s₁ - s₂ = 0

Question 33

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 to 25.44
C)-76.53 to 16.53
D)-102.83 to 42.43
E)98.45 to 125.48

Question 34

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 t value used for this is ___.

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

Question 35

A researcher wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores.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 the treatment.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 36

A researcher wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores.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 the treatment.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 37

Restaurateur Denny Valentine is evaluating two sites,Raymondville and Rosenberg,for his next restaurant.He wants to prove that Raymondville residents (population 1)dine out more often than Rosenberg residents (population 2).Denny plans to test this hypothesis using a random sample of 81 families from each suburb.His alternate hypothesis is ___.

A) $\sigma$ ₁² < $\sigma$ ₂²
B) $\mu$ ₁ - µ₂ > 0
C)p₁ - p₂ = 0
D) $\mu$ ₁ - $\mu$ ₂ = 0
E)s₁ - s₂ = 0

Question 38

Lucy Baker is analyzing demographic characteristics of two television programs,Lost (population 1)and Heroes (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 39

A researcher is interested in testing to determine if the mean of population one is greater than the mean of population two.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 items from population one resulting in a mean of 14.3 and a standard deviation of 3.4.He randomly selects a sample of 14 items from population two resulting in a mean of 11.8 and a standard deviation 2.9.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
D)1.321
E)2.321

Question 40

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 41

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: 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 42

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests,Claude Carter,Quality Assurance Manager,has recommended purchasing rods from Redding Rods,Inc.(population 1),rather than Stockton Steel (population 2),since Redding's rods had less variability in length.Recently,Stockton revised it rod shearing operation,and 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 43

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.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 44

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 45

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.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 46

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: 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 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 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 alternate 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 48

A statistician is being asked to test a new theory that the proportion of population A possessing a given characteristic is greater than the proportion of population B possessing the characteristic.A random sample of 600 from population A has been taken and it is determined that 480 possess the characteristic.A random sample of 700 taken from population B showed that 350 possess the characteristic.The observed z for this is ___.

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

Question 49

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 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 50

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 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 51

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 52

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests,Claude Carter,Quality Assurance Manager,has recommended purchasing rods from Redding Rods,Inc.(population 1),rather than Stockton Steel (population 2),since Redding's rods had less variability in length.Recently,Stockton revised it rod shearing operation,and 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) $\sigma$ ₁²= $\sigma$ ₂²
B) $\sigma$ ₁² $\neq$ $\sigma$ ₂²
C) $\sigma$ ₁² > $\sigma$ ₂²
D) $\sigma$ ₁² < $\sigma$ ₂²
E)s₁²< s₂²

Question 53

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 54

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests,Claude Carter,Quality Assurance Manager,has recommended purchasing rods from Redding Rods,Inc.(population 1),rather than Stockton Steel (population 2),since Redding's rods had less variability in length.Recently,Stockton revised it rod shearing operation,and 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 alternate hypothesis is ___.

A) $\sigma$ ₁²= $\sigma$ ₂²
B) $\sigma$ ₁² $\neq$ $\sigma$ ₂²
C) $\sigma$ ₁² > $\sigma$ ₂²
D) $\sigma$ ₁² < $\sigma$ ₂²
E)s₁²< s₂²

Question 55

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 this 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 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 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 57

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 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.Assuming $\alpha$ = 0.05,the critical z value is ___.

A)-1.96
B)-1.645
C)1.645
D)1.96
E)2.33

Question 59

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests,Claude Carter,Quality Assurance Manager,has recommended purchasing rods from Redding Rods,Inc.(population 1),rather than Stockton Steel (population 2),since Redding's rods had less variability in length.Recently,Stockton revised it rod shearing operation,and 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 60

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 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) $\sigma$ ₁²= $\sigma$ ₂²
B) $\sigma$ ₁² $\neq$ $\sigma$ ₂²
C) $\sigma$ ₁² > $\sigma$ ₂²
D) $\sigma$ ₁² < $\sigma$ ₂²
E)s₁²< s₂²

Question 62

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) $\sigma$ ₁²= $\sigma$ ₂²
B) $\sigma$ ₁² $\neq$ $\sigma$ ₂²
C) $\sigma$ ₁² > $\sigma$ ₂²
D) $\sigma$ ₁² < $\sigma$ ₂²
E)s₁²< s₂²

Question 63

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 64

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

Question 65

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests,Claude Carter,Quality Assurance Manager,has recommended purchasing rods from Redding Rods,Inc.(population 1),rather than Stockton Steel (population 2),since Redding's rods had less variability in length.Recently,Stockton revised it rod shearing operation,and 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 = 0.05 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 $\sigma$ ₁²= $\sigma$ ₂²
B)reject the null hypothesis $\sigma$ ₁² < $\sigma$ ₂²
C)do not reject the null hypothesis $\sigma$ ₁²= $\sigma$ ₂²
D)do not reject the null hypothesis $\sigma$ ₁² < $\sigma$ ₂²
E)do nothing

Question 66

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests,Claude Carter,Quality Assurance Manager,has recommended purchasing rods from Redding Rods,Inc.(population 1),rather than Stockton Steel (population 2),since Redding's rods had less variability in length.Recently,Stockton revised it rod shearing operation,and 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 $\sigma$ ₁²= $\sigma$ ₂²
B)reject the null hypothesis $\sigma$ ₁² < $\sigma$ ₂²
C)do not reject the null hypothesis $\sigma$ ₁²= $\sigma$ ₂²
D)do not reject the null hypothesis $\sigma$ ₁² < $\sigma$ ₂²
E)do nothing

Question 67

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests,Claude Carter,Quality Assurance Manager,has recommended purchasing rods from Redding Rods,Inc.(population 1),rather than Stockton Steel (population 2),since Redding's rods had less variability in length.Recently,Stockton revised it rod shearing operation,and 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 68

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 $\sigma$ ₁²= $\sigma$ ₂²
B)reject the null hypothesis $\sigma$ ₁² $\neq$ $\sigma$ ₂²
C)do not reject the null hypothesis $\sigma$ ₁²= $\sigma$ ₂²
D)do not reject the null hypothesis $\sigma$ ₁² $\neq$ $\sigma$ ₂²
E)maintain status quo

Question 69

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 $\sigma$ ₁²= $\sigma$ ₂²
B)reject the null hypothesis $\sigma$ ₁² $\neq$ $\sigma$ ₂²
C)do not reject the null hypothesis $\sigma$ ₁²= $\sigma$ ₂²
D)do not reject the null hypothesis $\sigma$ ₁² $\neq$ $\sigma$ ₂²
E)do nothing

Question 70

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