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Let n 1=100,x 1 =50,n 2 =100, and X 2 =30.
a. At the 0.05 level of significance, is there evidence of a significant difference between the two population proportions?
i. State the null and alternative hypotheses.
ii. What is the value of the test statistic?
iii. At a(alpha) =0.05, what is your conclusion?

Answer :

Final answer:

The question involves testing the difference between two population proportions using a Z-test with null hypothesis H0: p1 = p2 and alternative Ha: p1 ≠ p2. The test statistic would be a Z-score. At α = 0.05, the null hypothesis is rejected if the p-value is less than 0.05.

Explanation:

The question presented asks whether there is a significant difference between the proportions of two populations, which implies that we are looking at a hypothesis test for comparing two independent proportions using a Z-test. The information provided includes the sample sizes (n1 and n2), and the number of successes in each sample (x1 and x2).

Null and Alternative Hypotheses

The null hypothesis (H0) for this test assumes that there is no difference in the population proportions (p1 = p2). The alternative hypothesis (Ha) posits that there is a difference (p1 ≠ p2).

Test Statistic Value

The test statistic is calculated by comparing the observed sample proportions to the expected proportions under the null hypothesis, considering the combined variance of both samples. A Z-score is typically used for the test statistic in comparing proportions.

Conclusion at α = 0.05

If the p-value obtained from the test statistic is less than the significance level of 0.05, we would reject the null hypothesis and conclude that there is a significant difference between the two population proportions. Otherwise, we do not reject the null hypothesis.

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