Question

A college admissions director wishes to estimate the mean age of all students currently enrolled. In a random sample of 22 students, the mean age is found to be 21.4 years. From past studies, the ages of enrolled students are normally distributed with a standard deviation of 10.2 years. Construct a 90% confidence interval for the mean age of all students currently enrolled.

b. The standard deviation of the sample mean:

Answer 1

Solution:

a) The 90% confidence interval for population mean is given as follows:

Where, x̄ is sample mean, σ is population standard deviation, n is sample size and Z_(0.10/2) is critical z-value to construct 90% confidence interval.

We have, x̄ = 21.4 years, σ = 10.2 years, n = 22

Using Z-table we get, Z_(0.10/2) = 1.645

Hence, 90% confidence interval for the mean age of all students currently enrolled is,

The 90% confidence interval for the mean age of all students currently enrolled is (17.823 years, 24.977 years).

b) The standard deviation of the sample mean is given as follows:

Where, SD_x̄ is standard deviation of sample mean, σ is population standard deviation and n is sample size.

We have, σ = 10.2 years, n = 22

The standard deviation of the sample mean is 2.175.

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