Question

It is known that, nationally, doctors working for health maintenance organizations (HMOs) average 13.5 years of experience in their specialties, with a standard deviation of 7.6 years. The executive director of an HMO in a western state is interested in determining whether or not its doctors have less experience than the national average. A random sample of 150 doctors from HMOs shows a mean of only 10.9 years of experience. What is the T

Answer 1

The value of the test statistic is z = -4.19.

Explanation:

The test statistic is:

`z = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the expected value for the population mean,
`\sigma` is the standard deviation and n is the size of the sample.

Average 13.5 years of experience in their specialties, with a standard deviation of 7.6 years.

This means that
`\mu = 13.5, \sigma = 7.6`

A random sample of 150 doctors from HMOs shows a mean of only 10.9 years of experience.

This means that
`n = 150, X = 10.9`

What is the test statistic?

`z = (X - \mu)/((\sigma)/(√(n)))`

`z = (10.9 - 13.5)/((7.6)/(√(150)))`

`z = -4.19`

The value of the test statistic is z = -4.19.