To find out what people think, the Gallup Poll selected a random sample of 520 women and 506 men. The pollsters showed them a list of personal attributes and asked them to indicate whether each attribute was “generally more true of men or of women”. When asked about intelligence, 28% of the men thought men were generally more intelligent, but only 14% of the women agreed. Is there a gender gap in opinions about which sex is smarter? Describe and interpret all the information about this, including the percentage and CI of each sex, the percentage and CI of people who thought women were more intelligent, the percentage and CI of men who thought this, and the percentage and CI of women who thought this, the difference in percentages and the CI of this, the OR and CI, and the p value. Reach a final conclusion.
To determine if there is a gender gap in opinions about which sex is smarter based on the Gallup Poll, we need to analyze the provided information. Let's break it down step by step:
1. Sample size: The Gallup Poll selected a random sample of 520 women and 506 men.
2. Percentage and CI of people who thought men were more intelligent:
- Men who thought men were more intelligent: 28% (28% of 506 men = 141.68 men)
- 95% Confidence Interval (CI) for men: We do not have the information required to calculate the CI for men. We need the standard error or the sample size to determine it.
3. Percentage and CI of people who thought women were more intelligent:
- Women who thought women were more intelligent: 14% (14% of 520 women = 72.8 women)
- 95% Confidence Interval (CI) for women: We do not have the information required to calculate the CI for women. We need the standard error or the sample size to determine it.
4. Difference in opinions between men and women on intelligence:
- Percentage difference in opinions: 28% - 14% = 14%
- 95% Confidence Interval (CI) for the difference: We do not have the information required to calculate the CI for the difference. We need the standard errors or the sample sizes of both groups to determine it.
5. Odds Ratio (OR) and CI:
- To calculate the Odds Ratio and its Confidence Interval, we need the number of respondents for each combination of opinions (e.g., men who thought men were smarter, women who thought men were smarter, men who thought women were smarter, and women who thought women were smarter). From the information provided, we cannot determine these values, so we cannot calculate the OR and CI.
6. P-value: The p-value is a statistical measure that indicates the probability of observing the data (or more extreme) if there were no true association between gender and opinions on intelligence. Without the additional statistical data mentioned above, we cannot calculate the p-value.
From the information given, we can conclude that we do not have enough data to determine the confidence intervals, odds ratio, and p-value related to the gender gap in opinions about which sex is smarter. Therefore, we cannot reach a final conclusion based solely on the information provided.