Question

A simple random sample of 60 items resulted in a sample mean of 97. 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?

Answer 1

Solution-

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

(93.0 , 101.0)

◆ calculation-

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).

(94.14 , 99.86)

◆ calculation-

c. What is the effect of a larger sample size on the margin of error?

For n = 60 , Margin of error is 4.05

For n = 120 , Margin of error is 2.86

So, as sample size increases Margin of error decreases.

large sample size gives lower margin of error.