Deck 9: Inferences Based on a Two Samples: Confidence Intervals and Tests of Hypotheses

Question 1

Calculate the degrees of freedom associated with a small-sample test of hypothesis for $\left( \mu _ { 1 } - \mu _ { 2 } \right)$ , assuming $\sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 }$ and $n _ { 1 } = 13 , n _ { 2 } = 12 , s _ { 1 } = 1.3 , s _ { 2 } = 1.5$ .

A) 23
B) 25
C) 12
D) 11

Answer 1

23

Question 2

Consider the following set of salary data: $$\begin{array} { l r r } \hline & \text { Men (1) } & \text { Women (2) } \\\hline \text { Sample Size } & 100 & 80 \\\text { Mean } & \$ 12,850 & \$ 13,000 \\\text { Standard Deviation } & \$ 345 & \$ 500 \\\hline\end{array}$$ What assumptions are necessary to perform a test for the difference in population means?

A) The two samples were independently selected from the populations of men and women.
B) Both of the target populations have approximately normal distributions.
C) The population variances of salaries for men and women are equal.
D) All of the above are necessary.

Answer 2

The two samples were independently selected from the populations of men and women.

Question 3

Answer 3

A

Question 4

In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below: $$\begin{array} { l c c } \hline & \text { Sample Mean } & \text { Sample Variance } \\\hline \text { Adults (1) } & 77.5 ^ { \circ } \mathrm { F } & 4.5 \\\text { Children (2) } & 74.5 ^ { \circ } \mathrm { F } & 2.5 \\\hline\end{array}$$ Suppose that the psychologist decides to construct a 99% confidence interval for the difference in mean comfortable room temperatures instead of proceeding with a test of hypothesis. The 99% confidence interval turns out to be (-2.9, 3.1). Select the correct statement.

A) It cannot be concluded at the 99% confidence level that there is actually a difference between the true mean comfortable room temperatures for the two groups.
B) It can be concluded at the 99% confidence level that the true mean comfortable room temperature for children exceeds that for adults.
C) It can be concluded at the 99% confidence level that the true mean room temperature for adults exceeds that for children.
D) It can be concluded at the 99% confidence level that the true mean comfortable room temperature is between -2.9 and 3.1.

Question 5

Calculate the degrees of freedom associated with a small-sample test of hypothesis for $\left( \mu _ { 1 } - \mu _ { 2 } \right)$ , assuming $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ and $n _ { 1 } = n _ { 2 } = 12$

A) 23
B) 25
C) 12
D) 11

Question 6

Which of the following represents the difference in two population proportions?

Question 7

Which of the following represents the ratio of variances?

Question 8

When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex - males or females - is more likely to respond. Random, independent samples of 60 females and 100 males were each asked if they would be willing to give blood when called by a local hospital. A success is defined as a person who responds to the call and donates blood. The goal is to compare the percentage of the successes between the male and female responses. What type of analysis should be used?

A) A paired difference comparison of population means.
B) An independent samples comparison of population proportions.
C) A test of a single population proportion.
D) An independent samples comparison of population means.

Question 9

Calculate the degrees of freedom associated with a small-sample test of hypothesis for $\left( \mu _ { 1 } - \mu _ { 2 } \right)$ , assuming $\sigma _ { 1 } ^ { 2 } \approx \sigma _ { 2 } ^ { 2 }$ and $n _ { 1 } = n _ { 2 } = 20$

A) 30
B) 15
C) 31
D) 33

Question 10

Which of the following represents the difference in two population means?

A) μ1 - μ2
B) μ1 + μ2
C) p1 - p2
D) p1 + p2

Question 11

In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below: $$\begin{array} { l c c } \hline & \text { Sample Mean } & \text { Sample Variance } \\\hline \text { Adults (1) } & 77.5 ^ { \circ } \mathrm { F } & 4.5 \\\text { Children (2) } & 74.5 ^ { \circ } \mathrm { F } & 2.5 \\\hline\end{array}$$ Find the standard error of the estimate for the difference in mean comfortable room temperatures between adults and children.

A) 0.8367
B) 0.7000
C) 1.6279
D) 0.1871

Question 12

University administrators are trying to decide where to build a new parking garage on campus. The state legislature has budgeted just enough money for one parking structure on campus. The administrators have determined that the parking garage will be built either by the college of engineering or by the college of business. To help make the final decision, the university has randomly and independently asked students from each of the two colleges to estimate how long they usually take to find a parking spot on campus (in minutes). Based on their sample, the following 95% confidence interval (for μe - μb) was created - (4.20, 10.20). What conclusion can the university make about the population mean parking times based on this confidence interval?

A) They are 95% confident that the mean parking time of all business students exceeds the mean parking time of all engineering students.
B) They are 95% confident that the mean parking time of all business students is less than the mean parking time of all engineering students.
C) They are 95% confident that the mean parking time of all business students equals the mean parking time of all engineering students.

Question 13

Question 14

Independent random samples of 100 observations each are chosen from two normal populations with the following means and standard deviations. Population 1 Population 2

Question 15

A certain manufacturer is interested in evaluating two alternative manufacturing plans consisting of different machine layouts. Because of union rules, hours of operation vary greatly for this particular manufacturer from one day to the next. Twenty-eight random working days were selected and each plan was monitored and the number of items produced each day was recorded. Some of the collected data is shown below: $$\begin{array} { c | c | c } \text { DAY } & \text { PLAN 1 OUTPUT } & \text { PLAN 2 OUTPUT } \\\hline 1 & 1234 \text { units } & 1311 \text { units } \\2 & 1355 \text { units } & 1366 \text { units } \\3 & 1300 \text { units } & 1289 \text { units }\end{array}$$ What type of analysis will best allow the manufacturer to determine which plan is more effective?

A) A paired difference comparison of population means.
B) An independent samples comparison of population proportions.
C) A test of a single population proportion.
D) An independent samples comparison of population means.

Question 16

A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. It was desired to test to determine if the mean age of all female purchasers exceeds the mean age of all male purchasers. The sample data is shown here: Female: $\mathrm { n } = 10 , \quad$ sample mean $= 50.30 , \quad$ sample standard deviation $= 13.215$
Male: $\quad \mathrm { n } = 10 , \quad$ sample mean $= 39.80 , \quad$ sample standard deviation $= 10.040$ Which of the following assumptions must be true in order for the pooled test of hypothesis to be valid? I. Both the male and female populations of ages must possess approximately normal probability distributions. II. Both the male and female populations of ages must possess population variances that are equal. III. Both samples of ages must have been randomly and independently selected from their respective populations.

A) I only
B) II only
C) III only
D) I, II, and III

Question 17

Calculate the degrees of freedom associated with a small-sample test of hypothesis for $\left( \mu _ { 1 } - \mu _ { 2 } \right)$ , assuming
$\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 } \text { and } n _ { 1 } = n _ { 2 } = 16$

A) 30
B) 15
C) 31
D) 33

Question 18

Data was collected from CEOs of companies within both the low-tech industry and the consumer products industry. The following printout compares the mean return-to-pay ratios between CEOs in the low tech industry with CEOs in the consumer products industry. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM RETURN
industry 1 (low tech) $\quad ($ NUMBER $= 15$ )
industry $3 \quad$ (consumer products) $\quad$ (NUMBER $= 15 )$
$$\begin{array} { l } X = \text { industry1 } \\Y = \text { industry } 3\end{array}$$
$$\begin{array}{l}\text {SAMPLE MEAN OF X \( =157.286 \) }\\\text {SAMPLE VARIANCE OF \( X=1563.45 \)}\\\text {SAMPLE SIZE OF \( X=14 \)}\\\text {SAMPLE MEAN OF \( Y=217.583 \)}\\\text {SAMPLE VARIANCE OF \( Y=1601.54 \)}\\\text {SAMPLE SIZE OF \( Y=12 \)}\\\\\text { MEAN X - MEAN Y }=-60.2976 \\t=-4.23468 \\\text { P-VALUE }=0.000290753 \\\text { P-VALUE } / 2=0.000145377 \\\text { SD. } \text { ERROR }=14.239 \\\end{array}$$ If we conclude that the mean return-to-pay ratios of the consumer products and low tech CEOs are equal when, in fact, a difference really does exist between the means, we would be making a __________.

A) Type II error
B) Type I error
C) Type III error
D) correct decision

Question 19

A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. What type of analysis should be used to compare the mean age of male and female purchasers?

A) A paired difference comparison of population means.
B) An independent samples comparison of population proportions.
C) A test of a single population mean.
D) An independent samples comparison of population means. 9.2 Comparing Two Population Means: Independent Sampling
1 Understand Process of Comparing Two Independent Means

Question 20

Data was collected from CEOs of companies within both the low-tech industry and the consumer products industry. The following printout compares the mean return-to-pay ratios between CEOs in the low-tech industry with CEOs in the consumer products industry. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM RETURN
$\begin{array} { l l l } \text { industry } 1 & \text { (low tech) } & \text { (NUMBER } = 15 \text { ) } \\ \text { industry } 3 & \text { (consumer products) } & \text { (NUMBER } = 15 \text { ) } \end{array}$
$$\begin{array} { l } X = \text { industry1 } \\Y = \text { industry } 3\end{array}$$
$$\begin{array}{l}\text { SAMPLE MEAN OF X \( =157.286 \)}\\\text { SAMPLE VARIANCE OF \( X=1563.45 \)}\\\text { SAMPLE SIZE OF X \( =14 \)}\\\text { SAMPLE MEAN OF \( Y=217.583 \)}\\\text { SAMPLE VARIANCE OF \( Y=1601.54 \)}\\\text { SAMPLE SIZE OF Y \( =12 \)}\\\\\text { MEAN X - MEAN } Y=-60.2976 \\t=-4.23468 \\\mathrm{P}-\mathrm{VALUE}=\quad 0.000290753 \\\text { P-VALUE } / 2=0.000145377 \\\text { SD. } \mathrm{ERROR}=14.239 \\\end{array}$$ Using the printout, which of the following assumptions is not necessary for the test to be valid?

A) The population means are equal.
B) Both populations have approximately normal distributions.
C) The population variances are equal.
D) The samples were randomly and independently selected.

Question 21

Consider the following set of salary data:

Question 22

In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below:

Question 23

Consider the following set of salary data:

Question 24

The owners of an industrial plant want to determine which of two types of fuel (gas or electricity) will produce more useful energy at a lower cost. The cost is measured by plant investment per delivered quad ($ invested /quadrillion BTUs). The smaller this number, the less the industrial plant pays for delivered energy. Random samples of 11 similar plants using electricity and 16 similar plants using gas were taken, and the plant investment/quad was calculated for each. In an analysis of the difference of means of the two samples, the owners were able to reject H0 in the test H0: (μE - μG) = 0 vs. Ha: (μE - μG) > 0. What is our best interpretation of the result?

A) The mean investment/quad for electricity is greater than the mean investment/quad for gas.
B) The mean investment/quad for electricity is different from the mean investment/quad for gas.
C) The mean investment/quad for electricity is less than the mean investment/quad for gas.
D) The mean investment/quad for electricity is not different from the mean investment/quad for gas.

Question 25

The owners of an industrial plant want to determine which of two types of fuel (gas or electricity) will produce more useful energy at a lower cost. The cost is measured by plant investment per delivered quad ($ invested /quadrillion BTUs). The smaller this number, the less the industrial plant pays for delivered energy. Suppose we wish to determine if there is a difference in the average investment/quad between using electricity and using gas. Our null and alternative hypotheses would be:

Question 26

Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items common to each of two supermarkets (labeled A and B) and recorded the prices charged by each supermarket. The summary results are provided below: $$\begin{array} { l l r } \bar { x } _ { \mathrm { A } } = 2.09 & \bar { x } \mathrm {~B} = 1.99 & \bar { d } = .10 \\s _ { \mathrm { A } } = 0.22 & \mathrm {~s} _ { \mathrm { B } } = 0.19 & s _ { d } = .03\end{array}$$ Assuming a matched pairs design, which of the following assumptions is necessary for a confidence interval for the mean difference to be valid?

A) None of these assumptions are necessary.
B) The population of paired differences has an approximate normal distribution.
C) The population variances must be equal.
D) The samples are randomly and independently selected.

Question 27

In order to compare the means of two populations, independent random samples of 225 observations are selected from each population with the following results. Give the significance level, and interpret the result. 4 Conduct Pooled Hypothesis Test

Question 28

Assume that

Question 29

Independent random samples from normal populations produced the results shown below. Sample 1: 5.8, 5.1, 3.9, 4.5, 5.4 Sample 2: 4.4, 6.1, 5.2, 5.7

Question 30

Consider the following set of salary data: $$\begin{array} { l r r } \hline & \text { Men (1) } & \text { Women (2) } \\\hline \text { Sample Size } & 100 & 80 \\\text { Mean } & \$ 12,850 & \$ 13,000 \\\text { Standard Deviation } & \$ 345 & \$ 500 \\\hline\end{array}$$ Suppose the test statistic turned out to be z = -1.20 (not the correct value). Find a two-tailed p-value for this test statistic.

A) .2302
B) .3849
C) .1151
D) .6151

Question 31

A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. It was desired to test to determine if the mean age of all female purchasers exceeds the mean age of all male purchasers. The sample data is shown here: Female: n = 20, sample mean = 50.30, sample standard deviation = 13.215 Male: n = 20, sample mean = 39.80, sample standard deviation = 10.040 Use the pooled estimate of the population standard deviation to calculate the value of the test statistic to use in this test of hypothesis.

A) t = 2.17
B) t = 2.65
C) t = 2.83
D) t = 3.17

Question 32

A researcher is investigating which of two newly developed automobile engine oils is better at prolonging the life of an engine. Since there are a variety of automobile engines, 20 different engine types were randomly selected and were tested using each of the two engine oils. The number of hours of continuous use before engine breakdown was recorded for each engine oil. Based on the information provided, what type of analysis will yield the most useful information?

A) Matched pairs comparison of population means.
B) Matched pairs comparison of population proportions.
C) Independent samples comparison of population proportions.
D) Independent samples comparison of population means.

Question 33

University administrators are trying to decide where to build a new parking garage on campus. The state legislature has budgeted just enough money for one parking structure on campus. The administrators have determined that the parking garage will be built either by the college of engineering or by the college of business. To help make the final decision, the university has randomly and independently asked students from each of the two colleges to estimate how long they usually take to find a parking spot on campus (in minutes). Suppose that the sample sizes selected by the university for the two samples were both $\mathrm { n } _ { \mathrm { e } } = \mathrm { n } _ { \mathrm { b } } = 15$ . What critical value should be used by the university in the calculations for the 95% confidence interval for ?e - ?b? Assume that the university used the pooled estimate of the population variances in the calculation of the confidence interval.

A) z = 1.645
B) z = 1.96
C) t = 2.042
D) t = 2.048
E) t = 1.701

Question 34

Question 35

Question 36

Comment on the validity of the results.

Question 37

We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each brand of cola at each supermarket. The data are shown in the following table: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Price }$
$\begin{array}{l}\begin{array} { c | c c | c } \text { Supermarket } & \text { Brand 1 } & \text { Brand 2 } & \text { Difference } \\\hline 1 & \$ 2.25 & \$ 2.30 & \$ - 0.05 \\2 & 2.47 & 2.45 & 0.02 \\3 & 2.38 & 2.44 & - 0.06 \\4 & 2.27 & 2.29 & - 0.02 \\5 & 2.15 & 2.25 & - 0.10 \\6 & 2.25 & 2.25 & 0.00 \\7 & 2.36 & 2.42 & - 0.06 \\8 & 2.37 & 2.40 & - 0.03 \\\hline & \mathrm { x } _ { 1 } = 2.3125 & \mathrm { x } _ { 2 } = 2.3500 & \mathrm {~d} = - 0.0375 \\& \mathrm {~s} _ { 1 } = 0.1007 & \mathrm {~s} _ { 2 } = 0.0859 & \mathrm {~s} _ { \mathrm { d } } = 0.0381\end{array}\end{array}$ If the problem above represented a paired difference, what assumptions are needed for a confidence interval for the mean difference to be valid?

A) The population of paired differences has an approximately normal distribution.
B) The samples were independently selected from each population.
C) The population variances are equal.
D) All of the above are needed.

Question 38

Independent random samples selected from two normal populations produced the following sample means and standard deviations.

Question 39

In order to compare the means of two populations, independent random samples of 144 observations are selected from each population with the following results. Use a 95% confidence interval to estimate the difference between the population means (μ1 - μ2). Interpret the confidence interval.

Question 40

Independent random samples selected from two normal populations produced the following sample means and standard deviations.

Question 41

A researcher is investigating which of two newly developed automobile engine oils is better at prolonging the life of an engine. Since there are a variety of automobile engines, 20 different engine types were randomly selected and were tested using each of the two engine oils. The number of hours of continuous use before engine breakdown was recorded for each engine oil. Suppose the following 95% confidence interval for μA - μB was calculated: (100, 2500). Which of the following inferences is correct?

A) We are 95% confident that an engine using oil A has a higher mean number of hours of continuous use before breakdown than does an engine using oil B.
B) We are 95% confident that the mean number of hours of continuous use of an engine using oil A is between 100 and 2500 hours.
C) We are 95% confident that an engine using oil B has a higher mean number of hours of continuous use before breakdown than does an engine using oil A.
D) We are 95% confident that no significant differences exists in the mean number of hours of continuous use before breakdown of engines using oils A and B.

Question 42

Question 43

In order for the results of a paired difference experiment to be unbiased, the experimental units in each pair must be chosen independently of one another.

Question 44

A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let μ1 be the true mean weight of individuals before starting the diet and let μ2 be the true mean weight of individuals after 3 weeks on the diet. Calculate a 90% confidence interval for the difference between the mean weights before and after the diet is used.

Question 45

The data for a random sample of five paired observations are shown below.

Question 46

Question 47

Using paired differences removes sources of variation that tend to inflate $\sigma ^ { 2 }$ .

Question 48

$$\text { The sample mean difference } \bar { d } \text { is equal to the difference of the sample means } \bar { x } _ { 1 } - \bar { x } _ { 2 } \text {. }$$

Question 49

The data for a random sample of six paired observations are shown below.

Question 50

A paired difference experiment has 75 pairs of observations. What is the rejection region for testing Ha: μd > 0? Use α = .01.

Question 51

We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each brand of cola at each supermarket. The data are shown in the following table:

Question 52

A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let μ1 be the true mean weight of individuals before starting the diet and let μ2 be the true mean weight of individuals after 3 weeks on the diet.

Question 53

The sample standard deviation of differences sd is equal to the difference of the sample standard deviations $s _ { 1 } - s _ { 2 }$

Question 54

A certain manufacturer is interested in evaluating two alternative manufacturing plans consisting of different machine layouts. Because of union rules, hours of operation vary greatly for this particular manufacturer from one day to the next. Twenty-eight random working days were selected and each plan was monitored and the number of items produced each day was recorded. Some of the collected data is shown below: $$\begin{array} { c | c | c } \text { DAY } & \text { PLAN 1 OUTPUT } & \text { PLAN 2 OUTPUT } \\\hline 1 & 1234 \text { units } & 1311 \text { units } \\2 & 1355 \text { units } & 1366 \text { units } \\3 & 1300 \text { units } & 1289 \text { units }\end{array}$$ What assumptions are necessary for the above test to be valid?

A) The population of paired differences must be approximately normally distributed.
B) The population variances must be approximately equal.
C) Both populations must be approximately normally distributed.
D) None of these listed, since the Central Limit Theorem can be applied.

Question 55

An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the new coating, the inventor randomly selects one of the two tires on each of 50 bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to determine whether the new spray coating improves the wear of the bicycle tires. The data and summary information is shown below: 1 1.452 0.785

Question 56

A paired difference experiment has 15 pairs of observations. What is the rejection region for testing Ha: μd > 0? Use α = .05.

Question 57

An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the new coating, the inventor randomly selects one of the two tires on each of 50 bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to determine whether the new spray coating improves the wear of the bicycle tires. The data and summary information is shown below: 1 1.452 0.785

Question 58

An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the new coating, the inventor randomly selects one of the two tires on each of 50 bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to determine whether the new spray coating improves the wear of the bicycle tires. The data and summary information is shown below: 1 1.452 0.785

Question 59

Question 60

Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items common to each of two supermarkets (labeled A and B) and recorded the prices charged by each supermarket. The summary results are provided below:

Question 61

In an exit poll, 42 of 75 men sampled supported a ballot initiative to raise the local sales tax to build a new football stadium. In the same poll, 41 of 85 women sampled supported the initiative. Find and interpret the p-value for the test of hypothesis that the proportions of men and women who support the initiative are different.

Question 62

When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex - males or females - is more likely to respond. Random, independent samples of 60 females and 100 males were each asked if they would be willing to give blood when called by a local hospital. A success is defined as a person who responds to the call and donates blood. The goal is to compare the percentage of the successes of the male and female responses. Suppose 45 of the females and 60 of the males responded that they were able to give blood. Find the test statistic that would be used if it is desired to test to determine if a difference exists between the proportion of the females and males who responds to the call to donate blood.

A) z = 2.01
B) z = 1.645
C) z = 1.96
D) z = 1.93

Question 63

When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex - males or females - is more likely to respond. Random, independent samples of 60 females and 100 males were each asked if they would be willing to give blood when called by a local hospital. A success is defined as a person who responds to the call and donates blood. The goal is to compare the percentage of the successes of the male and female responses. Find the rejection region that would be used if it is desired to test to determine if a difference exists between the proportion of the females and males who responds to the call to donate blood. Use α = 0.10.

Question 64

A government housing agency is comparing home ownership rates among several immigrant groups. In a sample of 235 families who emigrated to the U.S. from Eastern Europe five years ago, 165 now own homes. In a sample of 195 families who emigrated to the U.S. from Pacific islands five years ago, 125 now own homes. Write a 95% confidence interval for the difference in home ownership rates between the two groups. Based on the confidence interval, can you conclude that there is a significant difference in home ownership rates in the two groups of immigrants?

Question 65

The FDA is comparing the mean caffeine contents of two brands of cola. Independent random samples of 6 -oz. cans of each brand were selected and the caffeine content of each can determined. The study provided the following summary information.

Question 66

Determine whether the sample sizes are large enough to conclude that the sampling distributions are approximately normal.

Question 67

A paired difference experiment produced the following results.

Question 68

A cola manufacturer invited consumers to take a blind taste test. Consumers were asked to decide which of two sodas they preferred. The manufacturer was also interested in what factors played a role in taste preferences. Below is a printout comparing the taste preferences of men and women. HYPOTHESIS: PROP. $\mathrm { X } =$ PROP. $Y$

SAMPLES SELECTED FROM soda(brand1,brand2)

$\begin{array}{lll}\text { males } & (\text { sex }=0, \text { males }) & (N U M B E R=115) \\\text { females } & (\text { sex }=1, \text { females }) & (\mathrm{NUMBER}=56)\end{array}$

$$\begin{array}{l}X=\text { males } \\Y=\text { females }\end{array}$$

$$\begin{array}{l}\text {SAMPLE PROPORTION OF X \( =0.422018 \)}\\\text {SAMPLE SIZE OF \( X=109 \)}\\\text {SAMPLE PROPORTION OF Y \( =0.25 \)}\\\text {SAMPLE SIZE OF Y \( =52 \)}\\\\\text {PROPORTION X - PROPORTIOIY=0.172018 }\\\text {Z=2.11825} \end{array}$$

Suppose the manufacturer wanted to test to determine if the males preferred its brand more than the females. Using the test statistic given, compute the appropriate p-value for the test.

A) .0170
B) .0340
C) .4681
D) .2119

Question 69

One indication of how strong the real estate market is performing is the proportion of properties that sell in less than 30 days after being listed. Of the condominiums in a Florida beach community that sold in the first six months of 2006, 75 of the 115 sampled had been on the market less than 30 days. For the first six months of 2007, 25 of the 85 sampled had been on the market less than 30 days. Test the hypothesis that the proportion of condominiums that sold within 30 days decreased from 2006 to 2007. Use α = .01.

Question 70

We sampled 100 men and 100 women and asked: "Do you think the environment is a major concern?" Of those sampled, 67 women and 53 men responded that they believed it is. For the confidence interval procedure to work properly, what additional assumptions must be satisfied?

A) Both samples were randomly and independently selected from their respective populations.
B) The population variances are equal.
C) Both populations have approximate normal distributions.
D) All of the above are necessary.

Question 71

A consumer protection agency is comparing the work of two electrical contractors. The agency plans to inspect residences in which each of these contractors has done the wiring in order to estimate the difference in the proportions of residences that are electrically deficient. Suppose the proportions of residences with deficient work are expected to be about .6 for both contractors. How many homes should be sampled in order to estimate the difference in proportions using a 95% confidence interval of width .8?

Question 72

The FDA is comparing the mean caffeine contents of two brands of cola. Independent random samples of 6 -oz. cans of each brand were selected and the caffeine content of each can determined. The study provided the following summary information.

Question 73

Construct a 90% confidence interval for

Question 74

A new type of band has been developed for children who have to wear braces. The new bands are designed to be more comfortable, look better, and provide more rapid progress in realigning teeth. An experiment was conducted to compare the mean wearing time necessary to correct a specific type of misalignment between the old braces and the new bands. One hundred children were randomly assigned, 50 to each group. A summary of the data is shown in the table. How many patients would need to be sampled to estimate the difference in means to within 28 days with probability 99%?

Question 75

Question 76

Suppose you want to estimate the difference between two population means correct to within 2.5 with probability 0.95. If prior information suggests that the population variances are both equal to the value 20, and you want to select independent random samples of equal size from the populations, how large should the sample sizes be?

Question 77

Determine whether the sample sizes are large enough to conclude that the sampling distributions are approximately normal.

Question 78

An experiment has been conducted at a university to compare the mean number of study hours expended per week by student athletes with the mean number of hours expended by non athletes. A random sample of 55 athletes produced a mean equal to 20.6 hours studied per week and a standard deviation equal to 5.3 hours. A second random sample of 200 non athletes produced a mean equal to 23.5 hours per week and a standard deviation equal to 4.3 hours. How many students would need to be sampled in order to estimate the difference in means to within 1.5 hours with probability 95%?

Question 79

Question 80

A paired difference experiment yielded the following results.