Question

Dominos Pizza for years made a claim that they would deliver your pizza within 30 minutes ("30 minutes or less") of your order being placed (provided you live within a certain radius of their restaurant). A group of college students make the ultimate sacrifice and order Dominos from the same location for 20 straight days for the good of statistics. They find a mean of 23.7 minutes and a standard deviation of 2.15.

A) In constructing a 95% confidence interval for mean wait time for Dominos Pizza delivery using the data collected by the students, would your critical value be a z* or a t*? Explain your answer.
B) Staying consistent with your answer to part A, construct a 95% confidence interval for mean wait time of Dominos Pizza delivery.
C) Do you think this confidence interval is accurate for Dominos Pizza in general? Why or why not?

Answer 1

a. t*

b. (22.87, 24.53)

c. yes

Explanation:

We have the following data:

mean = m = 23.7

standard deviation = sd = 2.15

x = 20

Thus:

a. The critical value would be t * since the value is m <30

b. whenever the mean is less than 30, the t distribution is used, for 95% confidence interval with degree of freedom = (x - 1) df

= 20 - 1

= 19

now, for this value we look in the table of t, we find that t * = 1.729

m + - t * (sd / x ^ 81/2))

replacing

23.7 + - 1.729 * (2.15 / 20 ^ (1/2))

23.7 + - 0.8312

then the inverval would be:

23.7 + 0.8312 = 24.5312

23.7 - 0.8312 = 22.8688

(22.87, 24.53)

c. yes, the interval is accurate since the mean of 23.7 is within this value