Question

A medical laboratory develops two different vaccines, Vaccine A and Vaccine B, both designed to provide immunity to a particular virus. (A person is immune if he/she does not get sick when exposed to the virus.)

Scientists at the lab suspect that Vaccine A is more effective than Vaccine B. This means that p1 > p2 , where

• p1 = proportion of all persons who take Vaccine A who subsequently become immune• p2 = proportion of all persons who take Vaccine B who subsequently become immune

Data from vaccine tests show that 201 out of 330 persons who take Vaccine A become immune, while 178 out of 330 persons who take Vaccine B become immune. Find answers using 5% significance.

21. Identify hypotheses. (a) HA: p1 <p2

H0: p1 ≥p2
(d) HA: (p1 − p2) > 0.05

H0: (p1 − p2) ≤ 0.05 22. Find the P-value.

(a) 0.035 (b) 0.042

(c) 0.05 (d) 0.0697

(e) 1.81

23. Decide.

(a) It is (b) It is (c) It is (d) It is

24. Interpret

(b) HA: p1 >p2H0: p1 ≤p2

(e) None of the answers is correct

(c) HA: p1 ̸=p2H0: p1 =p2

too risky to reject the alternative hypothesis.
too risky to reject the null hypothesis.
not too risky to reject the alternative hypothesis. not too risky to reject the null hypothesis.

the test.

1. (a) There is sufficient evidence to show that Vaccine A is at least 5% more effective than Vaccine B.

2. (b) There is not sufficient evidence to show that Vaccine A is at least 5% more effective than Vaccine B.

3. (c) There is sufficient evidence to show that Vaccine A is more effective than Vac- cine B.

4. (d) There is not sufficient evidence to show that Vaccine A is more effective than Vaccine B.

25. Interpret the MINITAB 90% confidence interval: With 90% confidence,

1. (a) Between 0.65% and 13.29% more persons will be immune if all persons use Vac-

   cine A rather than Vaccine B.

2. (b) Between 0.65% and 13.29% more persons will be immune if all persons use Vac- cine B rather than Vaccine A.

3. (c) 6.97% more persons will be immune if all persons use Vaccine A rather than Vaccine B.

4. (d) 6.97% more persons will be immune if all persons use Vaccine B rather than Vaccine A.

Answer 1