Question

If a 90% confidence interval for the difference of proportions contains some positive and some negative values, what can we conclude about the relationship between p1 and p2 at the 90% confidence level?

a. There is a negative difference between p1 and p2.
b. There is no difference between p1 and p2.
c. There is a positive difference between p1 and p2.
d. We cannot make a conclusion about the relationship between p1 and p2.

Answer 1

b. There is no difference between p1 and p2.

Explanation:

Given that a 90% confidence interval for the difference of proportions contains some positive and some negative values

i.e. confidence interval lower bound is negative and upper bound is positive

This confirms that 0 is contained in the confidence interval for difference of proporitons at 90%

Hence for the hypotheses

`H_0: p_1-p_2 =0\\\\H_a: p_1-p_2 \\eq 0`

we find that 0 is inside the confidence interval

This implies null hypothesis is accepted

Hence we conclude that there is no difference

b. There is no difference between p1 and p2.