Question

For problem 9.36, use alpha = 0.05 and solve for the probability of committing a type ii error for the following possible true alternative means. a. mu_a = 98.5 b. μ=98 c. mu_a = 9 d. mu_a =9( happens to the probability of committing a type ii error as the alternative value of the mean gets farther from the null hypothesized value of 100?

Answer 1

The probability of committing a Type II error decreases as the alternative value of the mean gets farther from the null hypothesized value of 100.

Step-by-step explanation:

The probability of committing a Type II error is the probability of failing to reject a null hypothesis when the alternative hypothesis is true. In this case, the null hypothesis is that the true mean is 100, and the alternative hypotheses are different values of the mean. As the alternative value of the mean gets farther from the null hypothesized value of 100, the probability of committing a Type II error decreases.

For example, if the true alternative mean is very close to the null hypothesized value of 100, the probability of committing a Type II error would be high. But if the true alternative mean is far from 100, the probability of committing a Type II error would be low. This is because as the difference between the true alternative mean and the null hypothesized value increases, the test becomes more sensitive to detecting the difference.