Question

Construct a 95​% confidence interval to estimate the population mean with x̅ =109 and σ=31 for the following sample sizes.

n =32

n =45

n =65

A) with 95​% confidence when n = 32, the population mean is between the lower limit ___ and upper limit ____ (round to 3 decimals)

B) with 95​% confidence when n = 45, the population mean is between the lower limit ___ and upper limit ____ (round to 3 decimals)

C) with 95​% confidence when n = 65, the population mean is between the lower limit ___ and upper limit ____ (round to 3 decimals)

Answer 1

Solution :

Given that,

A)

Sample size = n = 32

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z/2* ( /n)

= 1.96 * (31 / 32)

= 10.741

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

- E < < + E

109 - 10.741 < < 109 + 10.741

98.259 < < 119.741

lower limit = 98.259

upper limit = 119.741

B)

Margin of error = E = Z/2* ( /n)

= 1.96 * (31 / 45)

= 9.058

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

- E < < + E

109 - 9.058< < 109 + 9.058

99.942 < < 118.058

lower limit = 99.942

upper limit = 118.058

C)

Margin of error = E = Z/2* ( /n)

= 1.96 * (31 / 65)

= 7.536

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

- E < < + E

109 - 7.536 < < 109 + 7.536

101.464 < < 116.536

lower limit = 101.464

upper limit = 116.536