Question

A random sample of

nequals=12

values taken from a normally distributed population resulted in the sample values below. Use the sample information to construct

aa

95​%

confidence interval estimate for the population mean.

114114

104104

9191

109109

9696

104104

114114

100100

102102

103103

9494

108108

The

95​%

confidence interval is from

​$nothing

to

​$nothing

Answer 1

Solution:

Confidence interval for Population mean

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 103.25

S = 7.31281565

n = 12

df = n – 1 = 12 – 1 = 11

Confidence level = 95%

Critical t value = 2.2010

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 103.25 ± 2.2010*7.31281565/sqrt(12)

Confidence interval = 103.25 ± 2.2010*2.111028042

Confidence interval = 103.25 ± 4.6463

Lower limit = 103.25 - 4.6463 = 98.6037

Upper limit = 103.25 + 4.6463 = 107.8963

The 95% confidence interval is from 98.6037 to 107.8963.