Chapter 9.5, Problem 126E

Two-Tailed Hypothesis Tests and CIs. The following relationship holds between hypothesis tests and confidence intervals for one-mean t-procedures: For a two-tailed hypothesis test at the significance level α, the null hypothesis H₀: μ ₌  μ₀ will be rejected in favor of the alternative hypothesis H_a: μ > μ₀ if and only if μ₀ lies outside the (1 – α)-level confidence interval for μ. In each case, illustrate the preceding relationship by obtaining the appropriate one-mean t-interval (Procedure 8.2 on page 355) and comparing the result to the conclusion of the hypothesis test in the specified exercise.

1. a. Exercise 9.113
2. b. Exercise 9.116

9.113 TV Viewing. According to Communications Industry' Forecast & Report, published by Veronis Suhler Stevenson, the average person watched 4.55 hours of television per day in 2005. A random sample of 20 people gave the following number of hours of television watched per day for last year.

At the 10% significance level, do the data provide sufficient evidence to conclude that the amount of television watched per day

last year by the average person differed from that in 2005? (Note: = 4.760 hours and s = 2.297 hours.)

9.116 Apparel and Services. According to the document Consumer Expenditures, a publication of the Bureau of Labor Statistics, the average consumer unit spent $1736 on apparel and services in 2012. That same year, 25 consumer units in the Northeast had the following annual expenditures, in dollars, on apparel and services.

At the 5% significance level, do the data provide sufficient evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $17367? (Note: The sample mean and sample standard deviation of the data are $1922.76 and $350 90 respectively.)