Question

A medical experiment is PLANNED to compare the herb echinacea with a placebo for preventing colds. One response variable will be "volume of nasal secretions" (if you have a cold, you blow your nose a lot). Suppose the average volume of nasal secretions in people without colds is 3. An increase to 6 indicates a cold. (a) Which of the following describes the meaning of the significance level α for a test of the hypotheses: H0: μ = 3 versus Ha: μ > 3 ? α is the probability of selecting a sample whose data leads us to the decision to reject H0 when in reality μ = 3 is true. α is the probability of selecting a sample whose data leads us to the decision to reject H0 when in reality μ = 6 is true. α is the probability of selecting a sample whose data leads us to the decision to fail to reject H0 when in reality μ = 3 is true. α is the probability of selecting a sample whose data leads us to the decision fail to reject H0 when in reality μ = 6 is true. (b) The power of the test in (a) when the true value of the population mean is μ = 6 is The probability of selecting a sample whose data leads us to the decision to reject H0 when μ = 3 is true. The probability of selecting a sample whose data leads us to the decision to reject H0 when μ = 6 is true. The probability of selecting a sample whose data leads us to the decision to fail to reject H0 when μ = 3 is true. The probability of selecting a sample whose data leads us to the decision to fail to reject H0 when μ = 6 is true.

Answer 1

a) α is the probability of selecting a sample whose data leads us to the decision fail to reject H0 when in reality μ = 6 is true.

b) The power of the test in (a) when the true value of the population mean is μ = 6 is the probability of selecting a sample whose data leads us to the decision to reject H0 when μ = 6 is true.

Explanation:

Hello!

The objective of the experiment is to compare an herb against a placebo to test the effect of the herb for preventing colds.

Supposing:

Average nasal secretion volume of people without cold is 3

Average nasal secretion volume of people with a cold is 6

a)

If the hypotheses are:

H₀: μ = 3

H₁: μ >3

The level of significance "α" is the probability of committing a type I error. The type I error is defined as "not rejecting a false null hypothesis"

In this example, it would be the probability of not rejecting the null hypothesis when in reality the population mean is greater than 3.

b)

The power of the test, symbolized β, is the probability of rejecting a false null hypothesis.

In this example, this would mean to reject the null hypothesis when the average volume of nasal secretions is greater than 3.

I hope it helps!