Question

Independent random samples of size n1=38 and n2=86 observations, were selected from two populations. The samples from populations 1 and 2 produced x1=18 and x2=13 successes, respectively. Define p1 and p2 to be the proportion of successes in populations 1 and 2, respectively. We would like to test the following hypotheses: H0:p1=p2 versus H1:p1≠p2

(a)To test H0 versus H1, which inference procedure should you use?

A. Two-sample z procedure

B. One-sample z procedure

C. One-sample t procedure

D. Two-sample t procedure

(b) What is the standard error of (p̂ 1−p̂ 2) under the null hypothesis?

A. 0.0081

B. 0.0843

C. 0.0897

D. 0.0071

(c) What is the test statistic for this hypothesis test?

A. 1.960

B. 4.7379

C. 3.8256

D. 3.5953

(d) What is the P-value of this test?

A. Greater than 0.10

B. Between 0.05 and 0.10

C. Between 0.01 and 0.05

D. Less than 0.01

(e) Can we reject H0 in favour of H1 at the α=0.01 significance level?

A. Yes

B. No

C. We are unable to make a conclusion at this significance level.

Answer 1

The statistical software output for this problem is:

Hence,

a) Two Sample z procedure

b) Standard error = 0.0843

c) Test statistic = 3.8256

d) P value is less than 0.01

e) Yes