Question

he information below should be used to answer the following question.

The following hypothesis was tested at the .05 level with n = 64. The standard deviation for the scores was 20 and the mean of the sample was 104.

Ho: ? ? 100
Ha: ? > 100

If the true value of the population mean was equal to 105 instead of 100, what would be the probability of a Type II error?

		.641
		.567
		.433
		.359

Answer 1

For 0.05 level of significance, we get from the t distribution tables fo n-1 = 63 degrees of freedom that:

P( t₆₃ > 1.669 ) = 0.05

Therefore, the value of mean for which the null hypothesis would be rejected is computed as:

Now the probability of a type II error is computed as the probability of retaining a false null hypothesis. For a population mean of 105, the distribution for sample mean is computed as:

Converting this to a standard normal variable, we get:

Getting this from the standard normal tables, we get:

Therefore 0.359 must be the required probability of type II error here.