Question

Consider the hypothesis test below. ho: p1-p2 <=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
p-bar 0.24	p-bar 0.17

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 , what is your hypothesis testing conclusion?
- Select your answer -Conclude the difference between the proportions is greater than 0

   Cannot conclude the difference between the proportions is greater than 0

Answer 1

The pooled proportion(P) = ( * n1 + * n2)/(n1 + n2)

                                         = (0.24 * 200 + 0.17 * 300)/(200 + 300)

                                        = 0.198

a) The test statistic z = ()/sqrt(P(1 - P)(1/n1 + 1/n2))

                                  = (0.24 - 0.17)/sqrt(0.198 * (1 - 0.198) * (1/200 + 1/300))

                                  = 1.92

b) P-value = P(Z > 1.92)

                  = 1 - P(Z < 1.92)

                  = 1 - 0.9726 = 0.0274

c) At 0.05 significance level, since the P-value is less than the significance level(0.0274 < 0.05), so we should reject the null hypothesis.

Conclude the difference between the proportions is greater than 0.