Question

A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 72, 55, 49, 35, 39, 23, and 77. It can be assumed that weekday customer visits follow a normal distribution. [You may find it useful to reference the t table.]

a. Construct the 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to at least 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

b. Construct the 99% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to at least 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

c. What happens to the width of the interval as the confidence level increases?

A: As the confidence level increases, the interval becomes narrower and less precise.

Or

B: As the confidence level increases, the interval becomes wider and less precise.

Answer 1

	Values ( X )
	72	484
	55	25
	49	1
	35	225
	39	121
	23	729
	77	729
Total	350	2314

Mean

Standard deviation

Part a)

Confidence Interval



Lower Limit =
Lower Limit = 35.5765
Upper Limit =
Upper Limit = 64.4235
90% Confidence interval is ( 35.58 , 64.42 )
Width of CI = 64.42 - 35.58 = 25.84

part b)

Confidence Interval



Lower Limit =
Lower Limit = 22.4812
Upper Limit =
Upper Limit = 77.5188
99% Confidence interval is ( 22.48 , 77.52 )

Width of CI = 77.52 - 22.48 = 55.04

part c)

B: As the confidence level increases, the interval becomes wider and less precise.