Question

A simple random sample of 60 items resulted in a sample mean of 95. The population standard deviation is 13.

a. Compute the 95% confidence interval for the population mean (to 1 decimal).

(  ,  )

b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals).

(  ,  )

c. What is the effect of a larger sample size on the margin of error?
SelectIt increasesIt decreasesIt stays the sameIt cannot be determined from the given data

Answer 1

Solution :

Given that,

= 95

= 13

n = 60

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= 1.960 * (13 / 60 ) = 3.3

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

- E < < + E

95 - 3.3 < < 95 + 3.3

91.7 < < 98.3

(91.7 , 98.3)

b ) n = 120

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= 1.960 * (13 / 120 ) = 2.3

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

- E < < + E

95 - 2.3 < < 95 + 2.3

92.7 < < 97.3

(92.7 , 97.3)

c ) The effect of a larger sample size on the margin of error is decreasing .