Solved: In Exercises 11 14, test the claim about the difference between two population

What is the difference between two samples that are dependent and two samples that are independent? Give an example of each.

Explain how to perform a two-sample z@test for the difference between two population means using independent samples with s1 and s2 known.

Describe another way you can perform a hypothesis test for the difference between the means of two populations using independent samples with s1 and s2 known that does not use rejection regions.

What conditions are necessary in order to use the z@test to test the difference between two population means?

In Exercises 5 8, classify the two samples as independent or dependent. Explain your reasoning.Sample 1: The maximum bench press weights for 53 football players Sample 2: The maximum bench press weights for the same 53 football players after completing a weight lifting program

In Exercises 5 8, classify the two samples as independent or dependent. Explain your reasoning.Sample 1: The IQ scores of 60 females Sample 2: The IQ scores of 60 males

In Exercises 5 8, classify the two samples as independent or dependent. Explain your reasoning.Sample 1: The average speed of 23 powerboats using an old hull design Sample 2: The average speed of 14 powerboats using a new hull design

In Exercises 5 8, classify the two samples as independent or dependent. Explain your reasoning.. Sample 1: The commute times of 10 workers when they use their own vehicles Sample 2: The commute times of the same 10 workers when they use public transportation

In Exercises 9 and 10, use the TI-84 Plus display to make a decision to reject or fail to reject the null hypothesis at the level of significance. Make your decision using the standardized test statistic and using the P-value. Assume the sample sizes are equal.a = 0.05

In Exercises 9 and 10, use the TI-84 Plus display to make a decision to reject or fail to reject the null hypothesis at the level of significance. Make your decision using the standardized test statistic and using the P-value. Assume the sample sizes are equal.a = 0.01

In Exercises 11 14, test the claim about the difference between two population means m1 and m2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology Claim: m1 = m2; a = 0.1. Population statistics: s1 = 3.4 and s2 = 1.5 Sample statistics: x1 = 16, n1 = 29 and x2 = 14, n2 = 28

In Exercises 11 14, test the claim about the difference between two population means m1 and m2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology Claim: m1 7 m2; a = 0.10. Population statistics: s1 = 40 and s2 = 15 Sample statistics: x1 = 500, n1 = 100 and x2 = 495, n2 = 75

In Exercises 11 14, test the claim about the difference between two population means m1 and m2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology Claim: m1 6 m2; a = 0.05. Population statistics: s1 = 75 and s2 = 105 Sample statistics: x1 = 2435, n1 = 35 and x2 = 2432, n2 = 90

In Exercises 11 14, test the claim about the difference between two population means m1 and m2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology . Claim: m1 m2; a = 0.03. Population statistics: s1 = 136 and s2 = 215 Sample statistics: x1 = 5004, n1 = 144 and x2 = 4895, n2 = 156

Testing the Difference Between Two Means In Exercises 1524, (a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Braking Distances To compare the braking distances for two types of tires, a safety engineer conducts 35 braking tests for each type. The mean braking distance for Type A is 42 feet. Assume the population standard deviation is 4.7 feet. The mean braking distance for Type B is 45 feet. Assume the population standard deviation is 4.3 feet. At a = 0.10, can the engineer support the claim that the mean braking distances are different for the two types of tires? (Adapted from Consumer Reports)

Testing the Difference Between Two Means In Exercises 1524, (a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Meal-Replacement Diets To compare the amounts spent in the first three months by clients of two meal-replacement diets, a researcher randomly selects 20 clients of each diet. The mean amount spent for Diet A is $643. Assume the population standard deviation is $89. The mean amount spent for Diet B is $588. Assume the population standard deviation is $75. At a = 0.01, can the researcher support the claim that the mean amount spent in the first three months by clients of Diet A is greater than the mean amount spent in the first three months by clients of Diet B? (Adapted from Consumer Reports)

Testing the Difference Between Two Means In Exercises 1524, (a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Wind Energy An energy company wants to choose between two regions in a state to install energy-producing wind turbines. A researcher claims that the wind speed in Region A is less than the wind speed in Region B. To test the regions, the average wind speed is calculated for 60 days in each region. The mean wind speed in Region A is 14.0 miles per hour. Assume the population standard deviation is 2.9 miles per hour. The mean wind speed in Region B is 15.1 miles per hour. Assume the population standard deviation is 3.3 miles per hour. At a = 0.05, can the company support the researchers claim?

Testing the Difference Between Two Means In Exercises 1524, (a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Repair Costs: Washing Machines You want to buy a washing machine, and a salesperson tells you that the mean repair costs for Model A and Model B are equal. You research the repair costs. The mean repair cost of 24 Model A washing machines is $208. Assume the population standard deviation is $18. The mean repair cost of 26 Model B washing machines is $221. Assume the population standard deviation is $22. At a = 0.05, can you reject the salespersons claim?

Testing the Difference Between Two Means In Exercises 1524, (a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.ACT Scores The mean ACT score for 43 male high school students is 21.1. Assume the population standard deviation is 5.0. The mean ACT score for 56 female high school students is 20.9. Assume the population standard deviation is 4.7. At a = 0.01, can you reject the claim that male and female high school students have equal ACT scores? (Adapted from ACT, Inc.)

Testing the Difference Between Two Means In Exercises 1524, (a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.ACT Scores A guidance counselor claims that high school students in a college preparation program have higher ACT scores than those in a general program. The mean ACT score for 49 high school students who are in a college preparation program is 22.2. Assume the population standard deviation is 4.8. The mean ACT score for 44 high school students who are in a general program is 20.0. Assume the population standard deviation is 5.4. At a = 0.10, can you support the guidance counselors claim? (Adapted from ACT, Inc.)

Testing the Difference Between Two Means In Exercises 1524, (a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Home Prices A real estate agency says that the mean home sales price in Spring, Texas, is the same as in Austin, Texas. The mean home sales price for 25 homes in Spring is $127,414. Assume the population standard deviation is $25,875. The mean home sales price for 25 homes in Austin is $112,301. Assume the population standard deviation is $27,110. At a = 0.01, is there enough evidence to reject the agencys claim? (Adapted from RealtyTrac)

Testing the Difference Between Two Means In Exercises 1524, (a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Home Prices Refer to Exercise 21. Two more samples are taken, one from Spring and one from Austin. For 50 homes in Spring, x1 = $124,329. For 50 homes in Austin, x2 = $110,483. Use a = 0.01. Do the new samples lead to a different conclusion?

Testing the Difference Between Two Means In Exercises 1524, (a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Watching More TV? A sociologist claims that children ages 617 spent more time watching television in 1981 than children ages 617 do today. A study was conducted in 1981 to find the time that children ages 617 spent watching television on weekdays. The results (in hours per weekday) are shown below. Assume the population standard deviation is 0.6 hour. 2.0 2.5 2.1 2.3 2.1 1.6 2.6 2.1 2.1 2.4 2.1 2.1 1.5 1.7 2.1 2.3 2.5 3.3 2.2 2.9 1.5 1.9 2.4 2.2 1.2 3.0 1.0 2.1 1.9 2.2 Recently, a similar study was conducted. The results are shown below. Assume the population standard deviation is 0.5 hour. 2.9 1.8 0.9 1.6 2.0 1.7 2.5 1.1 1.6 2.0 1.4 1.7 1.7 1.9 1.6 1.7 1.2 2.0 2.6 1.6 1.5 2.5 1.6 2.1 1.7 1.8 1.1 1.4 1.2 2.3 At a = 0.05, can you support the sociologists claim? (Adapted from University of Michigans Institute for Social Research)

Testing the Difference Between Two Means In Exercises 1524, (a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology. Spending More Time Sleeping? A sociologist claims that children ages 1214 spent less time sleeping in 1981 than children ages 1214 do today. A study was conducted in 1981 to find the time that children ages 1214 spent sleeping on weekdays. The results (in hours per weekday) are shown below. Assume the population standard deviation is 0.5 hour. 7.3 7.5 7.7 7.8 6.9 7.9 8.3 7.9 8.0 8.3 7.4 8.5 7.9 6.8 8.2 7.1 7.9 7.6 8.0 8.0 Recently, a similar study was conducted. The results are shown below. Assume the population standard deviation is 0.4 hour. 9.2 9.1 10.0 9.3 9.6 8.0 9.5 8.2 9.0 8.6 9.2 9.2 8.9 9.1 8.4 9.0 8.8 9.1 8.6 9.0 At a = 0.01, can you support the sociologists claim? (Adapted from University of Michigans Institute for Social Research)

Getting at the Concept Explain why the null hypothesis H0: m1 = m2 is equivalent to the null hypothesis H0: m1 - m2 = 0.

Getting at the Concept Explain why the null hypothesis H0: m1 m2 is equivalent to the null hypothesis H0: m1 - m2 0.

Testing a Difference Other Than Zero Sometimes a researcher is interested in testing a difference in means other than zero. For instance, you may want to determine whether the difference between the mean annual salaries for a job differ by more than a certain amount between two states. In Exercises 27 and 28, you will test the difference between two means using a null hypothesis of H0: m1 - m2 = k, H0: m1 - m2 k, or H0: m1 - m2 k. The standardized test statistic is still z = 1x1 - x22 - 1m1 - m22 sx1 - x2 where sx1 - x2 = B s2 1 n1 + s2 2 n2 .Microbiologist Salaries Is the difference between the mean annual salaries of microbiologists in Maryland and California more than $10,000? To decide, you select a random sample of microbiologists from each state. The results of each survey are shown in the figure. Assume the population standard deviations are s1 = $8795 and s2 = $9250. At a = 0.05, what should you conclude? (Adapted from U.S. Bureau of Labor Statistics)

Testing a Difference Other Than Zero Sometimes a researcher is interested in testing a difference in means other than zero. For instance, you may want to determine whether the difference between the mean annual salaries for a job differ by more than a certain amount between two states. In Exercises 27 and 28, you will test the difference between two means using a null hypothesis of H0: m1 - m2 = k, H0: m1 - m2 k, or H0: m1 - m2 k. The standardized test statistic is still z = 1x1 - x22 - 1m1 - m22 sx1 - x2 where sx1 - x2 = B s2 1 n1 + s2 2 n2 .Registered Nurse Salaries Is the difference between the mean annual salaries of registered nurses in New Jersey and Delaware equal to $10,000? To decide, you select a random sample of registered nurses from each state. The results of each survey are shown in the figure. Assume the population standard deviations are s1 = $8345 and s2 = $7620. At a = 0.01, what should you conclude? (Adapted from U.S. Bureau of Labor Statistics) x1 = $75,820 n1 = 32 x2 = $70,820 n2 = 30

In Exercises 29 and 30, construct the indicated confidence interval for m1 - m2.Microbiologist Salaries Construct a 95% confidence interval for the difference between the mean annual salaries of microbiologists in Maryland and California using the data from Exercise 27.

In Exercises 29 and 30, construct the indicated confidence interval for m1 - m2.Registered Nurse Salaries Construct a 99% confidence interval for the difference between the mean annual salaries of registered nurses in New Jersey and Delaware using the data from Exercise 28.