The Caring Drug Company claims its aspirin tablets will relieve headaches faster than any other aspirin on the market. To determine whether Caring's claim is valid, random samples of size 25 are chosen each from aspirins made by Caring and the Sento Drug Company. An aspirin is given to each of the 50 randomly selected persons suffering from headaches and the number of minutes required for each to recover from the headache is recorded. The sample results of average number of recovery (in minutes) and the standard deviation of recovery are:

Caring (C):

Average number of Minutes = 8.4

Standard Deviation = 4.2

Sento (S):

Average number of Minutes = 8.9

Standard Deviation = 4.6

A 5% significance level test is performed to determine whether Caring's aspirin cures headaches significantly faster than Sento's aspirin. Assume population variances are equal.

In other words test the following hypotheses:

H_o: _C - _S 0 and H₁: _C - _S < 0

a) What is the critical value for this test? (3 marks)

b) What is the Decision Rule? (3 marks)

c) What is the value of pooled variance? (2 marks)

d) What is the Test Statistic? (3 marks)

e) What is the conclusion? (3 marks)