A statistics student was interested in investigating the average time it takes to get a pizza delivered to their house from the local pizzeria. Over a few weeks, a random sample of 10 delivery times (in minutes) was recorded.The data are displayed below:

18.7, 24.7, 31.5, 22.3, 17.9, 20.3, 28.4, 27.2, 19.6, 32.9

Summary Statistics: x = 24.35 minutes and s = 5.43.

(a)Calculate and interpret a 95% confidence interval for the mean delivery time. [6 Marks]

Note:You must clearly show that you have followed the "Step-by-Step Guide to Producing a Confidence Interval by Hand" given in the Lecture Workbook, Chapter 6. Use the t-procedures tool to find values for the t-multiplier and standard error.

(b)The student believes that, on average, pizzas from this pizzeria take more than 20 minutes to

arrive. Does the data support this? Briefly justify your answer. [1 Mark]