For several years the mean number of customers per day at a restaurant has been 142. Recently, the number of customers was counted on each of 29 randomly selected days. Over these days, the mean number of customers was 151.1 with standard deviation 26.3.
a.) Suppose we are looking for evidence that the mean number of customers has changed (increased or decreased). Carry out a formal test of significance. Be sure to write hypotheses, then use software to compute a p-value precisely (code is given below). Then reach a conclusion at the 5% level of significance.
b.) Based on the same data, construct a 95% confidence interval for the mean number of customers now. Is the number "142" in your interval? Connect this to your conclusion in (a.).
c.) Based on the same data, construct a 90% confidence interval for the mean number of customers now. Is the number "142" in your interval? Connect this to your conclusion in (a.).
d.) Thinking about your answers in (b.) and (c.), what level of confidence would you have to select so that the number "142" is right on the edge of your confidence interval? How does this relate to the p-value you obtained in (a.)? Construct this interval to demonstrate!