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
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.
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