A random sample of 1576 undergraduates enrolled in management ethics courses was asked to respond on a scale from 1 (strongly disagree) to 7 (strongly agree) to the proposition that senior corporate executives are interested in social justice. The sample mean response was 4.28, and the sample standard deviation was 1.26.
a. Test at the 10% significance level, against a two-sided alternative, the null hypothesis that the population mean is 4.
b. Find the probability of a 10%-level test not rejecting the null hypothesis when the true mean response is 3.85. What is the form of the decision rule? Determine the value for minus-zĪ±, zĪ±, or plus or minus Ā±zĪ±/2 as appropriate for this test. Calculate the test statistic. State the conclusion of this test. Do NOT reject the null hypothesis. There is NOT sufficient evidence to conclude that the population mean response is not equal to 4.
b. The probability of the test not rejecting the null hypothesis is _______ when the true mean response is 3.85.