Question

A very large study showed that aspirin reduced the rate of first heart attacks by 45%. A pharmaceutical company thinks it has a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug. Complete parts a through d below.

a) What is the null hypothesis the company will use?

A. The new drug is not more effective than aspirin.

B. The new drug is more effective than aspirin.

C. The new drug is less effective than aspirin.

D. The new drug is as effective as aspirin.

b) What is their alternative hypothesis?

A. The new drug is as effective as aspirin.

B. The new drug is not more effective than aspirin.

C. The new drug is less effective than aspirin.

D. The new drug is more effective than aspirin.

c) The company conducted the study and found that the group using the new drug had somewhat fewer heart attacks than those in the aspirin group. The P-value from the hypothesis test was 0.002. What do you conclude?

A. There is not sufficient evidence to conclude that the alternative hypothesis is true because the​ P-value was so large.

B. There is not sufficient evidence to conclude that the alternative hypothesis is true because the​ P-value was so small.

C.There is evidence to conclude that the alternative hypothesis is true because the​ P-value was so large.

D. There is evidence to conclude that the alternative hypothesis is true because the​ P-value was so small.

d) What would you have concluded if the P-value had been 0.42?

A.There is evidence to conclude that the alternative hypothesis is true because the​ P-value was so small.

B. There is not sufficient evidence to conclude that the alternative hypothesis is true because the​ P-value was so large.

C. There is evidence to conclude that the alternative hypothesis is true because the​ P-value was so large.

D.There is not sufficient evidence to conclude that the alternative hypothesis is true because the​ P-value was so

small.

Answer 1

Solution :

a) The null hypothesis that company will use would be as follows :

The new drug is not more effective than aspirin.

Hence, option (A) is correct.

b) The alternative hypothesis would be as follows :

The new drug is more effective than aspirin.

Hence, option (D) is correct.

c) We make conclusion as follows :

If p-value is so small (say less than 0.01), then we reject the null hypothesis.

If p-value is is large (say greater than 0.01), then we fail to reject the null hypothesis.

We have, p-value = 0.002, which is so small, therefore we shall reject the null hypothesis.

Hence, the conclusion would be as follows :

There is sufficient evidence to conclude that the alternative hypothesis is true because the​ P-value was so small.

Hence, option (D) is correct.

d) p-value = 0.42, which is so large, therefore we would be fail to reject the null hypothesis.

Hence, the conclusion would be as follows :

There is not sufficient evidence to conclude that the alternative hypothesis is true because the​ P-value was so large.

Hence, option (B) is correct.

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