Question8. The mean age of students at a certain college was 26.6 years old in 2005. An administrator thinks the mean age for online students differs from this value. She randomly surveys 56 online students and finds that the sample mean is 29.4 years with a standard deviation of 2.1 years. At the $1 \%$ level of significance $(\alpha=0.01)$, what can be concluded about the administrator's claim? Include the following steps in your test. - State the null and alternative hypotheses - Calculate the test statistic - Find the p-value - Make a decision whether to reject $\mathrm{H}_{0}$ - Write an interpretation of the results