Question

A simple random sample of 30 items resulted in a sample mean of 30. The population standard deviation is 15.

a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place.
( ,  )

b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places.
( ,  )

Answer 1

Given: Sample size = n = 30 Sample mean = = 30, Sample SD = s = 15

a. A 100(1-)% Confidence interval for the population mean can be obtained using the formula:

Critical value for t at 1 - 0.05 / 2 = 1 - 0.025 = 0.975 and for n - 1 = 30 - 1 = 29 df,

= (24.4, 35.6)

Hence, the 95% confidence interval for the population mean is (24.4, 35.6)

b. For n = 120, a 100(1-)% Confidence interval for the population mean can be obtained using the formula:

At ,

Critical value for t at 1 - 0.05 / 2 = 1 - 0.025 = 0.975 and for n - 1 = 120 - 1 = 119 df,

Using excel function,

We get t_0.975,119 = 1.98.

Substituting the values,

= (27.29,32.71)

Hence, the 95% confidence interval for the population mean is (27.29,32.71)