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06:23In 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
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
Constructing Confidence Intervals for μ1-μ2. When the sampling distribution for x̅1-x̅2 is approximated by a t-distribution and the populations have equal variances, you can construct a confidence interval for μ1-μ2, as shown below.
Construct the indicated confidence interval for μ1-μ2 . Assume the populations are approximately normal with equal variances.
Family Doctor
To compare the mean number of days spent waiting to see a family doctor for two large cities, you randomly select several people in each city who have had an appointment with a family doctor. The results are shown at the left. Construct a 90% confidence interval for the difference in mean number of days spent waiting to see a family doctor for the two cities. (Adapted from Merritt Hawkins)
Testing the Difference Between Two Means In Exercises 15–24, (a) identify the claim and state Ho 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.
Bed-in-a-Box To compare customer satisfaction with mattresses that are delivered compressed in a box and traditional mattresses, a researcher randomly selects 30 ratings of mattresses in boxes and 30 ratings of traditional mattresses. The mean rating of mattresses in boxes is 68.7 out of 100. Assume the population standard deviation is 6.6. The mean rating of traditional mattresses is 70.9 out of 100. Assume the population standard deviation is 5.6. At α=0.01, can the researcher support the claim that the mean rating of traditional mattresses is greater than the mean rating of mattresses in a box? (Adapted from Consumer Reports)
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?
