Question

A simple random sample of size

n equals n=40

is drawn from a population. The sample mean is found to be

x overbar equals x=121.2

and the sample standard deviation is found to be

s equals s=12.4.

Construct a​ 99% confidence interval for the population mean.

Find the lower and upper bounds.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 121.2

sample standard deviation = s = 12.4

sample size = n = 40

Degrees of freedom = df = n - 1 = 39

t _/2,df = 2.708

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

= 2.708 * (12.4 / 40)

Margin of error = E = 5.3

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

- E < < + E

121.2 - 5.3 < < 121.2 + 5.3

115.9 < < 126.5

(115.9 , 126.5)

Lower bound = 115.9

Upper bound = 126.5