Question

Centron, a pharmaceutical company, produces an allergy relief medication called Breezia. The company claims that the population standard deviation of the duration of Breezia's allergy relief is 2.50 hours. A scientist with the FDA suspects, however, that the standard deviation of the duration of Breezia's allergy relief is greater than (less consistent than) what the company claims.

The scientist obtains a random sample of 24 adults with allergy sensitivities, measures the duration of Breezia's allergy relief for each person, and calculates the sample standard deviation to be 3.25 hours.

Is there sufficient evidence to conclude that the standard deviation of the duration of Breezia's allergy relief is greater than (less consistent than) what the company claims? Use an α = 0.01 level of significance. Note: A normal probability plot and box plot indicate that the duration of allergy relief is normally distributed.

Question 1

State the null and alternative hypotheses (using symbols).

Question 2

Explain what it would mean for the scientist's study to make a Type I Error.

Question 3

Verify the requirements for this hypothesis test. Briefly show that each requirement is satisfied.

Question 4

Test the hypothesis using either the classical (test statistic) approach or the P-value approach. Show all steps to your approach. Then state whether you reject H 0 or do not reject H 0.

Question 5

Is there sufficient evidence to conclude that the standard deviation of the duration of Breezia's allergy relief is greater than (less consistent than) what the company claims? State your conclusion in one or two sentences.

Answer 1