Question

In the early 1900s, nutritionists believed people who ate no meat had lower blood pressure. in the population of all Americans, the average systolic blood pressure is 121.2 mmHg. you decide to test this by selecting vegetarians; the sample had an average systolic blood pressure of 3 mmHg, with a standard deviation of 3.2. Using a significance level of 0.01, the critical value is -2.821, and the observed test statistic is -4.842. We reject the null hypothesis p < 0.01. Which of the following corresponds to the power of the hypothesis test?

A. The likelihood of concluding that the average systolic blood pressure of vegetarians is significantly different from the national average, when really it is.

B. The likelihood of concluding that the average systolic blood pressure of vegetarians is significantly different from the national average, when really it is not.

C. The likelihood of concluding that the average systolic blood pressure of vegetarians is not significantly different from the national average, when really it is.

D. The likelihood of concluding that the average systolic blood pressure of vegetarians is not significantly different from the national average, when really it is not.

Answer 1

H_o : The average systolic blood pressure of vegetarians is not significantly different from the national average

H₁ : The average systolic blood pressure of vegetarians is significantly different from the national average

Power of the test = Probability of rejecting H₁ when H_o is true

Hence,

Correct option : D. The likelihood of concluding that the average systolic blood pressure of vegetarians is not significantly different from the national average, when really it is not.