An SRS of 16 households is selected in Houston and the number of remote controls per household is counted. The sample average number of remote controls is 7 and the sample standard deviation is 2.9. (Assume a Normal distribution for the number of remote controls per household.) A study in 1990 found that the mean number of remote controls is 9. Has the number has changed over time? a. What is the null and alternative hypothesis? b. What is the proper test statistic and its value? c. For a significance level of 5%, what is the cut-off value for this test? d. Find the p-value. e. What do you conclude? f. Suppose the remote-control manufacturers are concerned that the number has decreased. How does that change your test?