Lab 8a Hypothesis Testing Calculator Activity

STAT 1400 Lab 8a: Confidence Intervals and Hypothesis Testing Using the TI Calculator Name: _______________________ Lab 8A Principle 1: A value not in the confidence interval can be rejected as a possible value of the population parameter. A value in the confidence interval is an “acceptable” possibility for the value of a population parameter. Principle 2: When the confidence intervals in two different populations do not overlap, it is reasonable to conclude that the two populations are different. 1. Exercise Gear. A company sells exercise clothing and equipment on the Internet. To design clothing, data on physical characteristics of different types of customers is collected. The weight, in kilograms, of 24 female randomly selected runners are recorded: 62.8 56.9 68 49.1 56.3 54.7 50.4 53.9 56.9 65.2 58.7 64.3 60.7 62.6 54.4 54.8 52.3 58.9 48.6 62 56.8 57.4 64.3 57.7 a) Construct the 95% confidence interval for the mean weight of the population of all female runners. b) Based on this confidence interval, does a test of H 0 : μ = 56.3 H 1 : μ≠ 56.3 reject H 0 at the 5% significance level? Explain. (Use Principal 1) c) Give the t statistic and its p -value for this test. d) Based on the p -value, do you reject H 0 ? e) In general, what does the p -value tell you that the confidence interval does not? Lab 8a Page 1 of 3 Published by Columbus State Community College, 550 E. Spring St., Columbus, Ohio, 43215. Copyright © 2023 Columbus State Community College. All rights reserved.

2. A Government Audit. A local brewery distributes beer in bottles labeled 24 ounces. A government agency thinks that the brewery is cheating its customers. The agency selects 50 of these bottles, measures their contents, and obtains a sample mean of 23.75 ounces and sample standard deviation of 0.8 ounces. . Test the claim by the government agency that the population mean is less than 24 ounces at the 0.05 level of significance. a. State the appropriate null and alternative hypotheses. Explain how you decided the alternative. b. Give the t statistic and its p-value for this test. c. State your conclusion in context. d. If the test gives strong evidence against the null hypothesis, would you conclude that all bottles the distributed by local brewery have less than 24 ounces? Explain. e. Give the 90% confidence interval for the mean number of ounces of all bottles distributed by this brewery. Explain how this supports your hypothesis test conclusion. (Use Principal 1) Lab 8a Page 2 of 3 Published by Columbus State Community College, 550 E. Spring St., Columbus, Ohio, 43215. Copyright © 2023 Columbus State Community College. All rights reserved.