Question

A random sample of n=12 values taken from a normally distributed population resulted in the sample values below. Use the sample information to construct a 95% confidence interval estimate for the population mean.

99 102 95 97 109 97 110 102 95 108 98 97

The 95% confidence interval is from $_ to $_?

(round to two decimal places as needed. Use ascending order)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 100.75

sample standard deviation = s = 5.46

sample size = n = 12

Degrees of freedom = df = n - 1 = 12 - 1 = 11

t _/2,df = t_0.025,11 = 2.201

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

= 2.201 * ( 5.46/ 12)

Margin of error = E = 3.47

The 95% confidence interval estimate of the population mean is,

- E < < + E

100.75 - 3.47 < < 100.75 + 3.45

97.28 < < 104.22

(97.28 , 104.22)