A random sample of 1,562 undergraduates enrolled in management ethics courses was asked to respond, on a scale from 1 (strongly disagree) to 7 (strongly agree), to this proposition: Senior corporate executives are interested in social justice. The sample mean response was 4.27, and the sample standard deviation was 1.32.
a. Test at the 1% level, against a two-sided alternative, the null hypothesis that the population mean is 4.
b. Find the probability of a 1%-level test accepting the null hypothesis when the true mean response is 3.95.