Two proportions

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Independent samples give \widehat p_X and \widehat p_Y. The test of H_0:p_X=p_Y against H_1:p_X>p_Y has p-value 0.23. An approximate 99% confidence interval for p_X-p_Y is (-0.067,\,0.121).

1. State the hypotheses.

2. What does the p-value say at level 0.05?

3. Does the interval contain 0?

Worked answer (click to show)

H_0:p_X=p_Y against H_1:p_X>p_Y. The p-value 0.23 does not reject at level 0.05. The interval (-0.067,\,0.121) contains 0, which is the same conclusion.