Suppose you wish to determine if the mean IQ of students on your campus is different from the mean IQ in the general population, 100. To conduct this study, you obtain a simple random sample of 50 students on your campus, administer an IQ test, and record the results. The mean IQ of the sample of 50 students is found to be 107.3 with a standard deviation of 13.6.
(a) Conduct a hypothesis test (preferably using technology) H0: µ = µ0 versus H1: µ ≠ µ0 for
µ0 = 103, 104, 105, 106, 107, 108, 109, 110, 111, 112 at the α = 0.05 level of significance. For
which values of m0 do you not reject the null hypothesis?
(b) Construct a 95% confidence interval for the mean IQ of students on your campus. What
might you conclude about how the lower and upper bounds of a confidence interval relate to the
values for which the null hypothesis is rejected?
(c) Suppose you changed the level of significance in conducting the hypothesis test to α = 0.01.
What would happen to the range of values of m0 for which the null hypothesis is not rejected?
Why does this make sense? In Problems 23-29, decide whether the problem requires a
confidence interval or hypothesis test, and determine the variable of interest. For any problem
requiring a confidence interval, state whether the confidence interval will be for a population
proportion or population mean. For any problem requiring a hypothesis test, write the null and
alternative hypothesis.