Question

Suppose that we have collected a random sample of 49 breakfast orders from a major hotel chain, noting for each order how long the guest had to wait for the order to arrive once the order was placed. We find that, on average, guests had to wait 9.5 minutes for their breakfast order to be delivered. Additionally, it is known that the population standard deviation for the wait time of a breakfast order is 1.5 minutes. Use the information above to construct a 95% confidence interval for the population mean wait time of a breakfast order (in minutes). Once you have constructed such an interval, choose the values below that best correspond to your confidence interval. Note: Our experimental unit here is breakfast orders, not hotel guests.

a) (-9.92,-9.08)
b) (1.12, 1.88)
c) (9.08, 9.92)
d) (9.44, 9.56)
e) (-1.16, 4.16)

Answer 1

c) (9.08, 9.92)

Explanation:

The formula for Confidence interval =

Mean ± z + Standard deviation/√n

Mean = 9.5 minutes

Standard deviation = 1.5 minutes

n = random number of samples = 49

z = z score of 95% confidence interval = 1.96

Confidence interval = 9.5 ± 1.96 × 1.5/√49

Confidence interval = 9.5 ± 1.96 × 1.5/7

= 9.5 ± 0.420

Hence,

9.5 - 0.42

= 9.08

9.5 + 0.42

= 9.92

Therefore, the confidence interval =(9.08, 9.92). Hence, Option C is correct.