A hair salon in Cambridge, Massachusetts, reports that on seven randomly selecte
ID: 3361946 • Letter: A
Question
A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 62, 50, 31, 48, 54, 41, and 60. It can be assumed that weekday customer visits follow a normal distribution. Use Table 2.
Construct the 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. Round "t" value to 3 decimal places and final answers to 2 decimal places.)
Construct the 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. Round "t" value to 3 decimal places and final answers to 2 decimal places.)
What happens to the width of the interval as the confidence level increases?
A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 62, 50, 31, 48, 54, 41, and 60. It can be assumed that weekday customer visits follow a normal distribution. Use Table 2.
Explanation / Answer
a.
The average number of customers who visit the salon on weekdays, m = 49.43
Sample standard deviation of number of customers who visit the salon on weekdays, SD = 10.83
Standard error of sample mean = SD / sqrt(n) = 10.83 / sqrt(7) = 4.0934
Degree of freedom = n - 1 = 7 - 1 = 6
t value for 90% confidence interval and df = 6 is 1.943
Margin of error = SE * t = 4.0934 * 1.943 = 7.9535
90% confidence interval is
(49.43 - 7.9535, 49.43 + 7.9535)
(41.48, 57.38)
b.
t value for 99% confidence interval and df = 6 is 3.707
Margin of error = SE * t = 4.0934 * 3.707 = 15.1742
90% confidence interval is
(49.43 - 15.1742, 49.43 + 15.1742)
(34.26, 64.60)
c.
We see that the width of 99% confidence interval (64.6 - 34.26 = 30.34) is greater than 90% confidence interval (57.38 - 41.48 = 15.9)
So,
As the confidence level increases, the interval becomes wider and less precise.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.