Question

A random sample of

91

observations produced a mean

x=26.2

and a standard deviation

s=2.6

a. Find a​ 95% confidence interval for

μ.

b. Find a​ 90% confidence interval for

μ.

c. Find a​ 99% confidence interval for

μ.

Answer 1

Solution :

(a)

t _/2,df = 1.987

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

= 1.987 * (2.6 / 91)

Margin of error = E = 0.5

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

- E < < + E

26.2 - 0.5 < < 26.2 + 0.5

25.7 < < 26.7

(25.7 , 26.7)

(b)

t _/2,df = 1.662

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

= 1.662 * (2.6 / 91)

Margin of error = E = 0.5

The 90% confidence interval estimate of the population mean is,

- E < < + E

26.2 - 0.5 < < 26.2 + 0.5

25.7 < < 26.7

(25.7 , 26.7)

(c)

t _/2,df = 2.632

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

= 2.632 * (2.6 / 91)

Margin of error = E = 0.7

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

- E < < + E

26.2 - 0.7 < < 26.2 + 0.7

25.5 < < 26.9

(25.5 , 26.9)