Some students were asked, "Would you date someone with a great personality even though you did not find that person to be attractive?" Of the 131 women surveyed, 61.1% said yes, and of the 61 men surveyed, 42.6% said yes. Is there sufficient evidence to conclude that, for the populations represented by these students, a higher proportion of women would answer yes to this question? Test at the 5% level.

1. Let the women be Group 1, and let the men be Group 2. What is the parameter in the context of the problem?

2. Let the women be Group 1, and let the men be Group 2. Give the null and alternative hypotheses.

3. The test statistic was calculated to be 2.43. What is the p-value?

4. Based on your p-value, what is your statistical decision?

5. At the 5% level of significance, do we have sufficient evidence to say that, for the populations represented by these students, a higher proportion of women answer yes to this question? (Yes, No, or Maybe)

1. The parameter in the context of the problem is the proportion of students who would answer "yes" to the question about dating someone with a great personality but not finding them attractive. We are comparing this proportion between the two groups: women (Group 1) and men (Group 2).

2. Null hypothesis (H0): The proportion of women who would answer "yes" is equal to the proportion of men who would answer "yes."
Alternative hypothesis (Ha): The proportion of women who would answer "yes" is greater than the proportion of men who would answer "yes."

3. To calculate the p-value, we need to determine the probability of obtaining a test statistic value as extreme as 2.43 or more extreme, assuming the null hypothesis is true. The p-value is the probability of observing data that favors the alternative hypothesis. Since this is a one-sided test (greater than), we look up the p-value for the given test statistic value (2.43) in the t-distribution table or calculate it using statistical software or online calculators.

4. Without knowing the degrees of freedom or the exact sample sizes, we cannot provide the p-value or make a statistical decision. However, based on the given test statistic value of 2.43, if the p-value is less than the significance level of 0.05 (5%), we would reject the null hypothesis in favor of the alternative hypothesis.

5. Based on the information provided, we do not have enough information to determine the p-value or make a statistical decision. Therefore, we cannot conclude whether there is sufficient evidence to say that a higher proportion of women answer "yes" to this question at the 5% level of significance.