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 2. An increase to 6 indicates a cold.

(a) Which of the following describes the meaning of the significance level ? for a test of the hypotheses: H0: mu = 2 versus Ha: mu > 2 ?

a) alpha is the probability of selecting a sample whose data leads us to the decision to reject H0 when in reality mu = 2 is true.

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

(b) The power of the test in (a) when the true value of the population mean is mu = 6 is

a) The probability of selecting a sample whose data leads us to the decision to reject H0when mu = 6 is true.

b) The probability of selecting a sample whose data leads us to the decision to fail to reject H0 when mu = 2 is true.

(a) the significance level alpha is the probability of selecting a sample whose data leads us to the decision to reject H0 when in reality mu = 2 is true.

(b) The power of the test in (a) when the true value of the population mean is mu = 6 is The probability of selecting a sample whose data leads us to the decision to reject H0when mu = 6 is true.

Step-by-step explanation:

(a) When the hypothesis is H0: mu = 2 versus Ha: mu > 2, then p-value of sample mean is checked in a distribution assumed under null hypothesis. If the p value falls below the significance level, this means that the assumptions of null hypothesis is wrong.

(b) The probability of correctly rejecting H0 when it is false is known as the power of the test.