Question

A simple random sample of 60 items resulted in a sample mean of 89. The population...

A simple random sample of 60 items resulted in a sample mean of 89. The population standard deviation is 18.

a. Compute the 95% confidence interval for the population mean

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

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

-increase - decrease -same - cannot determine

a)

 sample mean 'x̄= 89 sample size    n= 60 std deviation σ= 18 std error ='σx=σ/√n= 2.3238
 for 95 % CI value of z= 1.960 margin of error E=z*std error = 4.55 lower bound=sample mean-E= 84.4455 Upper bound=sample mean+E= 93.5545
 from above 95% confidence interval for population mean =(84.45,93.55)

b)

 sample size    n= 120 std deviation σ= 18 std error ='σx=σ/√n= 1.6432
 for 95 % CI value of z= 1.960 margin of error E=z*std error = 3.22 lower bound=sample mean-E= 85.7795 Upper bound=sample mean+E= 92.2205
 from above 95% confidence interval for population mean =(85.78,92.22)

c)

effect of a larger sample size on the margin of error : decrease