A random small sample of 15 novels making a national best seller list was selected. The...

A random small sample of 15 novels making a national best seller list was selected. The average length of time these novels stayed on the best seller list was 5.2 weeks with standard deviation 2.3 weeks. Find the 99% conﬁdence interval for the average number of weeks a book is on the best seller list

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Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 5.2

sample standard deviation = s = 2.3

sample size = n = 15

Degrees of freedom = df = n - 1 = 15 - 1 = 14

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t_/2,df = t_0.005,14 = 2.977

Margin of error = E = t_/2,df * (s / $\sqrt$ n)

= 2.977 * (2.3 / $\sqrt$ 15)

= 1.8

The 99% confidence interval estimate of the population mean is,

- E < < + E

5.2 - 1.8 < < 5.2 + 1.8

3.4 < < 7.0

(3.4 , 7.0)

orchestra answered 1 year ago

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