This is Introduction to probability and statistics.

Please answer all parts clearly showing all the steps. (Please do not use excel, minitab, ...)

4. A business owner wants to test whether the total wait time at his two restaurants ('Pizza for everyone', and 'Burger Haven') are similar with one another. A random sample of eight customers' wait times was monitored from the two restaurants. The data below reect the time in minutes. Suppose \"1 denotes the mean wait time for restaurant 1 and #1 denotes the mean wait time for restaurant 2. Assume both population distributions are normal. Pizza for W one 5.2 4.3 6.7 7.8 3.9 5.0 6.3 4.7 7.1 8.3 4.7 3.9 4.6 5.4 6.0 6.3 4a. Calculate whether the variances are equal with a=0.05. a. (3 points) 4b. Regardless of what you concluded for 4a, test whether there is a signicant difference between the two restaurants' wait times. Use a 95% condence interval. (4 points)