High cholesterol is diagnosed if the mean level in blood is over 240. The amount

Question

High cholesterol is diagnosed if the mean level in blood is over 240. The amount of cholesterol in a blood sample varies from sample to sample but is almost normally distributed with mean (which is unknown) and standard deviation -10 . we test the hypothesis H0 240 against Ha: > 240 . A person is said to have very high cholesterol if their mean level is over 260, A person has 100 blood samples are taken and the sample mean evaluated. The test is done at the 5% level, and the null is NOT rejected. From the power analysis what conclusions can be we draw about the cholesterol level of that person? The power for the test is over 99.999%, therefore there is a 99.999% chance this person has very high cholesterol. The power for the test is less than 0.0001%. Therefore we are unsure of whether the person has VERY high cholesterol or not. As we did not reject the null, we do not know whether the patient has high cholesterol or not. However, as the power is over 99.999%, we can be relatively sure that the patient does not have VERY high cholesterol

Explanation / Answer

The correct option is B

Increase the sample size

Expalanation:

Increasing sample size makes the hypothesis test more sensitive - more likely to reject the null hypothesis when it is, in fact, false. Thus, it increases the power of the test. The effect size is not affected by sample size. And the probability of making a Type II error gets smaller, not bigger, as sample size increases.

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