In a 2017 probability sample of 2,023 people aged fifteen to twenty-four, the Public Religion Research Institute (PRRI) found that 37% of young women and 30% of young men had volunteered for a group or cause they cared about. Say that PRRI surveyed 1,072 women and 951 men.

a. The students in a political science class decide to calculate 80% confidence intervals around both proportions to see if they overlap. Calculate the standard errors for young men and women.

b. The class uses the standard errors from Part a to calculate the margins of error for the confidence intervals using this formula: . They calculate the margin of error to be .013 for both men and women. Use the formula for margin of error to find the z-score that the students used for the confidence interval.

c. What is the area in the normal table associated with the z-score that you found for Part b?

d. How can you tell that the students used the wrong z-score? What z-score should they have used?

e. Recalculate the margins of error for the confidence intervals using the correct z-score and the standard errors that you found for Part a.

f. Give the 80% confidence intervals for both sample proportions.
g. Is there evidence that young women are actually more likely to volunteer for causes they care about? Explain your answer.