A group of non-governmental organizations (NGOs) are collaborating to learn about whether men and women are affected differently by armed conflict in their countries. The group focuses their efforts on the effects of the civil war in Yemen.

The NGOs assemble a team of 150 researchers to collect information from adults who remained in Yemen and those who fled their homes for other countries.

a. The researchers collected samples of 500 men and women. In these samples, 90% of women experienced malnutrition at some point since the start of the conflict in Yemen, compared to 89% of men. What is the null hypothesis for this test?

b. The researchers conducted a two-sample test and calculated a sample z-score of 2.5. Use the formula for sample z to show what the standard error of the difference in proportions is.

c. The researchers find the p-value associated with the sample z-score of 2.5 and fail to reject the null hypothesis, at the .01 alpha-level. Did the researchers conduct a one- or two-tailed hypothesis test? Explain how you know.

d. The researchers drew their samples from a population of people who have been heavily displaced by war. What could this mean for the reliability of the results of the hypothesis test?