Question

Consider the hypothesis test below.

H ₀:  p ₁ -  p ₂  0  
H _a:  p ₁ -  p ₂ > 0

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

Sample 1	Sample 2
n1 = 100	n2 = 300
p1 = 0.24	p2 = 0.13

Use pooled estimator of p.

1. What is the value of the test statistic (to 2 decimals)?  
   
   
2. What is the  p-value (to 4 decimals)?  
   
   
3. With   = .05, what is your hypothesis testing conclusion?

Answer 1

The given null and alternative hypothesis are:

Test-statistic for the hypothesis is:

where,

pooled estimator of p

(a) calculation for test-statistic:

The test-statistic is calculated as

(b) p-value:

Since it is a one-tailed test, so the p-value is-

The p-value for the test is

(c) Decision:

Since,

Conclusion: At significance level of there is sufficient evidence to support the alternative hypothesis , i.e., . So, we conclude that the true population proportion of population 1 is greater than the population proportion of population 2.