Question

A simple random sample of 60 items resulted in a sample mean of 79. 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?

Answer 1

a)

95% confidence interval =75.7 ; 82.3

b)

standard errror of mean =

σx=σ/√n=

1.1867

for 95 % CI value of z=				1.960
margin of error E=z*std error                            =				2.326
lower confidence bound=sample mean-margin of error=				76.67
Upper confidence bound=sample mean +margin of error=				81.33

95% confidence interval =76.7 ; 81.3

c)

increasing sample size decreases margin of error,