Question

Suppose a null hypothesis is that the population mean is greater than or equal to 100. Suppose further that a random sample of 48 items is taken and the population standard deviation is 14. For each of the following a values, compute the probability of committing a type II error if the population mean actually is 99?

Answer 1

To compute the probability of committing a type II error, calculate the power of the test by using the normal distribution.

Step-by-step explanation:

To compute the probability of committing a type II error, we need to calculate the power of the test. The power of a statistical test is the probability of correctly rejecting the null hypothesis when it is false.

In this case, the null hypothesis is that the population mean is greater than or equal to 100. The alternative hypothesis is that the population mean is less than 100. The significance level (alpha) is the probability of committing a type I error.

Using the normal distribution and the given information, we can calculate the test statistic (z-score) and the critical value. Then, we can find the area under the curve to determine the power of the test.