I am working on a homework question and got stumped on this question.
- Suppose researchers perform a large-sample test of a population proportion where the null hypothesis is that the population proportion is 0.4, and the alternative hypothesis is that the population proportion is not equal to 0.4 (two-sided). They obtain a z-statistic of -1.5 under the null hypothesis.
a) (*1 point) What is the (two-sided) p-value? Choose the best answer: i) Two-sided p-value < 0.05 ii) 0.05 < Two-sided p-value < 0.32 iii) Two-sided p-value > 0.32 iv) Two-sided p-value > 0.68 v) Two-sided p-value > 0.95 vi) Two-sided p-value = -1.5
b) (*1 point) Would the 68% confidence interval include 0.4? Explain your answer.
For part a I said that the two-sided p value is in between 0.05 and 0.32 since the z-score is -1.5. However, I am not sure on how to solve the second part with this limited information. I was thinking since the p-value is not enough to reject the null hypothesis, 0.4 would be included, but I want to prove it mathematically. Thanks for any assistance.