Question

A mean equal to 5 cm. A simple random sample of wrist breadths of 40 women has a mean of 5.07

cm. The population standard deviation is 0.33 cm. Find the value of the test statistic?

Answer 1

The value of the test statistic is
`z = 1.34`

Explanation:

The test statistic is:

`z = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis,
`\sigma` is the standard deviation and n is the size of the sample.

Test if the mean is equal to 5:

This means that the null hypothesis is
`\mu = 5`

A simple random sample of wrist breadths of 40 women has a mean of 5.07 cm. The population standard deviation is 0.33 cm.

This means that
`n = 40, X = 5.07, \sigma = 0.33`

Find the value of the test statistic?

`z = (X - \mu)/((\sigma)/(√(n)))`

`z = (5.07 - 5)/((0.33)/(√(40)))`

`z = 1.34`

The value of the test statistic is
`z = 1.34`