Question

A simple random sample of 60 items resulted in a sample mean of 65. The population standard deviation is 16. 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?

3 diff Answers

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 65

Population standard deviation = = 16

Sample size = n = 60

Z_/2 = 1.96

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

= 1.96 * (16 / 60)

= 4.05

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

- E < < + E

65 - 4.05 < < 65 + 4.05

60.95 < < 69.05

( 60.95 , 69.05)

Sample size = n = 60

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

= 1.96 * (16 / 120)

= 2.86

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

- E < < + E

65 - 2.86 < < 65 + 2.86

62.14 < < 67.86

( 62.14 , 67.86)

the effect of a larger sample size on the margin of error will decreases