A hair salon in Cambridge, Massachusetts, reports that on seven randomly selecte
ID: 3365837 • 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 40, 30, 28, 22, 36, 16, and 50. 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 40, 30, 28, 22, 36, 16, and 50. It can be assumed that weekday customer visits follow a normal distribution. Use Table 2.
Explanation / Answer
a).
Calculation
M = 31.7143
t = 1.64
sM = (11.39762/7) = 4.31
= M ± Z(sM)
= 31.7143 ± 1.64*4.31
= 31.7143 ± 7.085845
Result
M = 31.7143, 90% CI [24.628455, 38.800145].
You can be 90% confident that the population mean () falls between 24.628455 and 38.800145.
(b)
Calculation
M = 31.7143
t = 2.58
sM = (11.39762/7) = 4.31
= M ± Z(sM)
= 31.7143 ± 2.58*4.31
= 31.7143 ± 11.096384
Result
M = 31.7143, 99% CI [20.617916, 42.810684].
You can be 99% confident that the population mean () falls between 20.617916 and 42.810684.
(c) As the confidence level increases, the interval becomes narrower and less precise.
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