Question

A hypothesis will be used to test that a population mean equals 5 against the alternative that the population mean is less than 5 with known variance σ. What is the critical value for the test statistic for the significance level of 0.010

Answer 1

The critical value is
`Z_c = -2.327`

Explanation:

A hypothesis will be used to test that a population mean equals 5 against the alternative that the population mean is less than 5

Test if the mean is less than a value, so a one-tailed hypothesis test is used.

Known variance σ.

This means that the z-distribution is used to solve this question.

What is the critical value for the test statistic for the significance level of 0.010?

Z with a p-value of 0.01, so, looking at the z-table,
`Z_c = -2.327`