Question

Suppose that competing hypotheses for a test are H0: p1 - p2 = 0 versus HA: p1 - p2 ≠ 0. A 95% confidence interval for the difference between the population proportions is calculated as [0.25, 0.40]. At the 5% significance level, the correct conclusion to the hypothesis test is

Answer 1

Answer:

Step-by-step explanation:

Given that in a hypothesis test for comparison of two proportions p1 and p2

two tailed at 95% confidence level

the confidence interval was (0.25,0.40)

The hypothesis was for

H0: p1 - p2 = 0 versus HA: p1 - p2 ≠ 0

As per null hypothesis the difference between proportions should be 0.

In our confidence interval we find lower limit is 0.25 and upper limit is 0.40

i.e. 0 is not contained in this interval and 0 is significantly far from this 0.25 even lower limit

So we can conclude that the difference between proportions cannot be 0 but is positive

So reject null hypothesis.

There is significant difference between proportions at 95% confidence level