please help, I cannot figure out this problem Twelve different video games showi

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please help, I cannot figure out this problem

Twelve different video games showing substance use were observed and the duration times of game play (in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. Use the sample data to construct a 95% confidence interval estimate of the mean duration of game play. 4051 3880 3860 4033 4323 4816 4661 4036 5003 4828 4336 4325

a) What is the confidence interval estimate of the population mean ?

b) Use the sample data to construct a 99% confidence interval estimate of ?, the standard deviation of the duration times of game play.

____ >>____ (round to one decimal place as needed)

Explanation / Answer

here sample size is n=12 which is less than 30, so we use t-distribution to calculate the confidence interval.

(a) (1-alpha)*100% confidence interval for population mean =sample mean±t(alpha/2,n-1)*sd/sqrt(n)

95% confidence interval for population mean=sample mean±t(0.05/2, 12-1)*sd/sqrt(n)

=4346±2.2*395.38/sqrt(12)=4346±251.1=(4094.9, 4597.1)

(b) 99% confidence interval for population mean=sample mean±t(0.01/2, 12-1)*sd/sqrt(n)

=4346±3.11*395.38/sqrt(12)=4346±354.96=(3991.04, 4700.96)

sample standard deviation=s=395.38

using ms-excel following information has been generated from the given data

x 4051 3880 3860 4033 4323 4816 4661 4036 5003 4828 4336 4325 mean= 4346 n= 12 s= 395.38

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