Question

A random sample of n=100 observations produced a mean of x̅=25 with a standard deviation of s=4.

(a) Find a 90% confidence interval for μ, z for 90 percentile : 1.28

(b) Find a 95% confidence interval for μ, z for 95 percentile : 1.75

(c) Find a 99% confidence interval for μ, z for 99 percentile : 2.33

Answer 1

 

Point estimate = sample mean = = 25

Population standard deviation = = 4

Sample size = n = 100

a)

At 90% confidence level the z is ,

z = 1.28

Margin of error = E = Z_/2* ( /√n)

=1.28 * (4 / √ 100 )

= 0.512

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

- E < < + E

25 - 0.512 < < 25 + 0.512

24.488 < < 25.512

( 24.488 , 25.512 )

b)

At 95% confidence level the z is ,

z = 1.75

Margin of error = E = Z_/2* ( /√n)

=1.75 * (4 / √ 100 )

= 0.70

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

- E < < + E

25 - 0.70 < < 25 + 0.70

24.30 < < 25.70

( 23.30 , 25.70 )

c)

At 99% confidence level the z is ,

z = 2.33

Margin of error = E = Z_/2* ( /√n)

= 2.33 * (4 / √ 100 )

= 0.932

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

- E < < + E

25 - 0.932 < < 25 + 0.932

24.068 < < 25.932

( 24.068 , 25.932 )