Chapter 7: Q20E (page 403)
If a hypothesis test were conducted using α= 0.05, for which of the following p-values would the null hypothesis be rejected?
a. .06
b. .10
c. .01
d. .001
e. .251
f. .042
The null hypothesis would be rejected for every case because all of the given p-values are less than the α value.
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Libor interest rate. The interest rate at which London banks lend money to one another is called the London interbank offered rate, or Libor. The British Bankers Association regularly surveys international banks for the Libor rate. One recent report (Bankrate.com, March 16, 2016) had the average Libor rate at 1.2% for 1-year loans—a value considered high by many Western banks. Set up the null and alternative hypotheses for testing the reported value.
What is the level of significance of a test of hypothesis?
-Question:Consumers’ use of discount coupons. In 1894, druggist Asa Candler began distributing handwritten tickets to his customers for free glasses of Coca-Cola at his soda fountain. That was the genesis of the discount coupon. In 1975, it was estimated that 65% of U.S. consumers regularly used discount coupons when shopping. In a more recent consumer survey, 81% said they regularly redeem coupons (NCH Marketing Services 2015 Consumer Survey). Assume the recent survey consisted of a random sample of 1,000 shoppers.
a. Does the survey provide sufficient evidence that the percentage of shoppers using cents-off coupons exceeds 65%? Test using α = 0.05.
b. Is the sample size large enough to use the inferential procedures presented in this section? Explain.
c. Find the observed significance level for the test you conducted in part a and interpret its value.
Latex allergy in health care workers (cont’d). Refer to Exercise 7.120. Let \({\sigma ^2}\) represent the variance in the number of latex gloves used per week by all hospital employees. Consider testing \({H_0}:{\sigma ^2} = 100\) against\({H_a}:{\sigma ^2} \ne 100.\)
a. Give the rejection region for the test at a significance level of\(\alpha = 0.01.\)
b. Calculate the value of the test statistic.
c. Use the results, parts a and b, to make the appropriate conclusion.
A t-test is conducted for the null hypothesis versus the alternative for a random sample of n = 17 observations. The test results are t = 1.174, p-value = 0.1288.
a. Interpret the p-value.
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