Question

A 99% confidence interval for the difference between two proportions was estimated at 0.11, 0.39. Based on this, we can conclude that the two population proportions are equal.

Answer 1

`\hat p_1 -\hat p_2 \pm z_(\alpha/2) SE`

And for this case the confidence interval is given by:

`0.11 \leq p_1 -p_2 \leq 0.39`

Since the confidenc einterval not contains the value 0 we can conclude that we have significant difference between the two population proportion of interest 1% of significance given. So then we can't conclude that the two proportions are equal

Explanation:

Let p1 and p2 the population proportions of interest and let
`\hat p_1` and
`\hat p_2` the estimators for the proportions we know that the confidence interval for the difference of proportions is given by this formula:

`\hat p_1 -\hat p_2 \pm z_(\alpha/2) SE`

And for this case the confidence interval is given by:

`0.11 \leq p_1 -p_2 \leq 0.39`

Since the confidence interval not contains the value 0 we can conclude that we have significant difference between the two population proportion of interest 1% of significance given. So then we can't conclude that the two proportions are equal