When the necessary conditions are met,a two-tail test is being conducted to test the difference between two population proportions.The two sample proportions are p₁ = 0.25 and p₂ = 0.20,and the standard error of the sampling distribution of p₁ - p₂ is 0.04.The calculated value of the test statistic will be: A) z = 0.25. B) z = 1.25. C) t = 0.25. D) t = 0.80.

Question

Quizplus · Accepted Answer

Since the standard error is given, we can use the formula:

test statistic = (sample proportion difference - hypothesized proportion difference) / standard error

Here, the hypothesized proportion difference is 0 (since we are testing for a difference) and the sample proportion difference is 0.25 - 0.20 = 0.05. Plugging in the values, we get:

test statistic = 0.05 / 0.04 = 1.25

Since this is a two-tail test, we need to find the critical values for a significance level (alpha) of 0.05. Looking at a standard normal distribution table or using a calculator, we find that the critical values are approximately -1.96 and 1.96. Since our test statistic (1.25) is not within this range, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference between the two population proportions. The correct answer is therefore (B).

When the Necessary Conditions Are Met,a Two-Tail Test Is Being