Chapter 7: Q1E (page 397)
Which hypothesis, the null or the alternative, is the status-quo hypothesis? Which is the research hypothesis?
The null hypothesis is a statement that represents the status-quo hypothesis.
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Student loan default rate. The national student loan default rate has fluctuated over the past several years. Recently (October 2015) the Department of Education reported the default rate (i.e., the proportion of college students who default on their loans) at 0.12. Set up the null and alternative hypotheses if you want to determine if the student loan default rate this year is less than 0.12.
The testing claimed by the national student loan default rate is the test for a specified proportion.
A t-test is conducted for the null hypothesis
a. Interpret the p-value.
Hotelsโ use of ecolabels. Refer to the Journal of Vacation Marketing (January 2016) study of travelersโ familiarity with ecolabels used by hotels, Exercise 2.64 (p. 104). Recall that adult travelers were shown a list of 6 different ecolabels, and asked, โSuppose the response is measured on a continuous scale from 10 (not familiar at all) to 50 (very familiar).โ The mean and standard deviation for the Energy Star ecolabel are 44 and 1.5, respectively. Assume the distribution of the responses is approximately normally distributed.
a. Find the probability that a response to Energy Star exceeds 43.
b. Find the probability that a response to Energy Star falls between 42 and 45. c. If you observe a response of 35 to an ecolabel, do you think it is likely that the ecolabel was Energy Star? Explain.
a. List three factors that will increase the power of a test.
b. What is the relationship between b, the probability of committing a Type II error, and the power of a test?
Managers who engage in โcoopetition.โ In business, firms that both cooperate and compete with other firms are described as engaging in โcoopetition.โ A study published in Industrial Marketing Management (February 2016) examined the level of external tension experienced by managers who engage in coopetition. External tension (measured on a 20-point scale) was recorded for each in a sample of 1,532 managers, all from firms that were engaged in coopetition. The sample mean tension was x=10.82 and the sample standard deviation was s=3.04.
Conduct a test (using a=.05) to determine if the true mean external tension level of all managers who engage in coopetition differs from 10.5 points.
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