Question

Consider the hypothesis test below.

Ho:p1-p2<equal 0

Ha:p1-p2>0

The following results are for independent samples taken from the two populations.

Sample 1	Sample 2
n1=200	n2=300
p1=.22	p2=0.14

Use pooled estimator of .
a. What is the value of the test statistic (to 2 decimals)?


b. What is the -value (to 4 decimals)?


c. With a=0.05, what is your hypothesis testing conclusion?
- Select your answer -Conclude the difference between the proportions is greater than 0Cannot conclude the difference between the proportions is greater than 0Item 3

Answer 1

Given that, the null and alternative hypotheses are,

H0 : p1 - p2 ≤ 0

Ha : p1 - p2 > 0

For sample 1 : n1 = 200 and p1-hat = 0.22

For sample 2 : n2 = 300 and p2-hat = 0.14

Pooled proportion is,

a) Test statistic is,

=> Test statistic = Z = 2.32

b) P-value = P(Z > 2.32) = 1 - P(Z < 2.32) = 1 - 0.9898 = 0.0102

=> p-value = 0.0102

c) Since, p-value = 0.0102 is less than a=0.05, we reject the null hypothesis.

Conclusion : we conclude the difference between the proportions is greater than 0.