A university president believes that, over the past few years, the average age of students attending his university has changed. To test this hypothesis, an experiment is conducted in which the age of 20 students, who have been randomly sampled from the student body, is measured. The mean age of these 20 students is 25 years. A complete census taken at the university a few years before the experiment showed a mean age of 23 years, with a standard deviation of 7. Assume that the population standard deviation is 7 and the population data are normally distributed.

(a) State the suitable null and alternative hypotheses that address the research question.

(b) Compute the z-statistic for our sample data. Show work.

(c) Based on the z-statistic, compute the p-value. Show work and attach R code.

(d) Suppose 0.05. Based on the p-value, decide whether you can reject the null.

(e) Using the same level, compute the upper critical value for the z-test. Show work and attach R code.

(f) Compare the upper z-critical with the z-statistic and decided whether you can reject the null. Did you reach the same conclusion as part (d)?

(g) Compute the 95% confidence intervals for the mean.