Parks and Mental Health In Exercises 13–18, use the figure, which shows the percentages from a survey of two hundred 18- to 24-year-olds in the United States who say that various park and recreation activities have a positive impact on their mental health. (Adapted from National Recreation and Park Association)





Exercising and Taking Classes At α=0.01, can you reject the claim that the proportion of 18- to 24-year-olds who benefit mentally from exercising in parks is greater than or equal to the proportion who benefit mentally from taking classes in parks?

Testing the Difference Between Two Means, (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 t, (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.

Pet Food

A pet association claims that the mean annual costs of food for dogs and cats are the same. The results for samples of the two types of pets are shown at the left. At , α=0.10 can you reject the pet association’s claim? Assume the population variances are equal. (Adapted from American Pet Products Association)

Testing a Difference Other Than Zero Sometimes a researcher is interested in testing a difference in means other than zero. In Exercises 27 and 28, you will test the difference between two means using a null hypothesis of Ho: μ1-μ2=k, Ho: μ1-μ2>=k or Ho: μ1-μ2<=k . The standardized test statistic is still

Architect Salaries Is the difference between the mean annual salaries of entry level architects in Denver, Colorado, and Lincoln, Nebraska, equal to \(9000? To decide, you select a random sample of entry level architects from each city. The results of each survey are shown in the figure. Assume the population standard deviations are σ1=\)6560 and σ2=\$6100 . At α=0.01 what should you conclude? (Adapted from Salary.com)

In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions and at the level of significance . Assume the samples are random and independent.

Claim: p1≠p2, α=0.01

Sample statistics: x1=35, n1=70, and x2=36, n2=60

Independent and Dependent Samples In Exercises 5–8, classify the two samples as independent or dependent and justify your answer.

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

Constructing Confidence Intervals for μd To construct a confidence interval for μd , use the inequality below.

Construct the indicated confidence interval for μd . Assume the populations are normally distributed.

[APPLET] Drug Testing A sleep disorder specialist wants to test the effectiveness of a new drug that is reported to increase the number of hours of sleep patients get during the night. To do so, the specialist randomly selects 16 patients and records the number of hours of sleep each gets with and without the new drug. The table shows the results of the two-night study. Construct a 90% confidence interval for μd.

Test the claim about the difference between two population means and at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ1=μ2, α=0.01, Assume (σ1)^2=(σ2)^2

Sample statistics:

x̅1=33.7, s1=3.5 , n1=12 and x̅2=35.5 , s2=2.2 , n2=17