A hair salon in Cambridge, Massachusetts, reports that on seven randomly selecte

Question

A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 52, 67, 33, 44, 54, 26, and 66. It can be assumed that weekday customer visits follow a normal distribution. Use Table 2. a. Construct a 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places and "t" value to 3 decimal places, and final answers to 2 decimal places.) Confidence interval to b. Construct a 99% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places and "t" value to 3 decimal places, and final answers to 2 decimal places.) Confidence interval to c. What happens to the width of the interval as the confidence level increases? As the confidence level increases, the interval becomes narrower and less precise. As the confidence level increases, the interval becomes wider and less precise.

Explanation / Answer

a) From information, xbar=48.86, s=15.58

90% c.i=xbar+-tcriticalSE(xbar), where, xbar ismeana number of customers visiting the salon, s is standard deviation of number of customers and t i s t critical at df=6(n=1) and alpha=0.10.

SE(xbar)=s/sqrt n, wher n is sample size.

=15.58/sqrt 7

=5.89

90% c.i=48.86+-1.943*5.89

=37.41 to 60.30

b) 99% c.i=48.86+-3.707*5.89

=27.02 to 70.69

c) A confidence level increases, interval becomes wider and less precise.

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