Question

John Pizza Restaurant is facing a stiff competition from the new competing pizza

restaurant guaranteeing pizza deliveries within 32 minutes or the pizza is given free. To

answer this challenge, Maldini wants to offer a 30-minute delivery guarantee. After a

careful cost analysis, Maldini has determined that such a guarantee would require an

average delivery time of less than 27 minutes. She thought that this would limit the

percentage of ‘free pizzas’ under the guarantee to less than 8% of all the deliveries, which

she had figured to be the break-even point for such a promotion. To find out if the

restaurant can meet these requirements, Maldini collected data on the total delivery times

and ‘free pizzas’ for a random sample of 81 orders within a month. The total delivery

time includes the preparation-time, the wait-time, and the travel-time for the drivers. The

sample data show an average total delivery time of 26.7 minutes with estimated

population standard deviation of 1.2 minutes. The data also show that 4 out of the 81

orders resulted in ‘free pizza’ deliveries because they took longer than 30 minutes to

deliver. Maldini is using a non-conventional confidence level of 97% in her estimates.

Please answer the following questions using the information given in this problem.

a.

Please calculate and interpret the 97% confidence interval for the mean total delivery

time of pizzas for the Maldini Restaurant. Please show the necessary steps

.

[2 points]

b. Please also calculate and interpret the 97% confidence interval for the proportion of

‘free pizzas’ expected under Maldini’s proposed promotion scheme. Please show the

necessary steps

. [2 points]

c. Based on the results for the two confidence intervals you calculated above, do you

think Maldini’s proposed promotion scheme is viable? Please carefully justify your

answer.

Answer 1

(a)

26.700	mean 1
1.200	std. dev.
0.133	std. error
81	n
80	df
26.405	confidence interval 97.% lower
26.995	confidence interval 97.% upper
0.295	margin of error

The 97% confidence interval for the mean total delivery time of pizzas for the Maldini Restaurant is between 26.405 and 26.995.

(b)

Observed
0.0494	p (as decimal)
4/81	p (as fraction)
4.	X
81	n
0.0556	std. error
-0.0029	confidence interval 97.% lower
0.1016	confidence interval 97.% upper
0.0522	margin of error

The 97% confidence interval for the proportion of ‘free pizzas’ expected under Maldini’s proposed promotion scheme is between -0.0029 and 0.1016.

(c) Based on the results for the two confidence intervals, Maldini’s proposed promotion scheme is viable.