Question

Suppose a hypothesis states that the mean is exactly 50. If a random sample of 35 items is taken to test this hypothesis, what is the value of β if the population standard deviation is 7 and the alternative mean is 53? Use alpha = 0.

Answer 1

To find the value of β in a hypothesis test with a known standard deviation, we need to determine the probability of making a Type II error.

Step-by-step explanation:

To find the value of β, we need to determine the probability of making a Type II error in the hypothesis test. A Type II error occurs when we fail to reject the null hypothesis when it is actually false.

In this case, the null hypothesis states that the mean is exactly 50, and the alternative hypothesis is that the mean is 53. The population standard deviation is given as 7.

To calculate β, we need to find the cutoff value of the test statistic that corresponds to rejecting the null hypothesis at a significance level of 0. This value can be found using the z-table or a statistical software.