A recent poll asked people whether they supported passing a constitutional amendment to ban burning of the national flag using a 1 to 100 scale."1" means that they do not support passing the amendment at all and "100" means they support it completely. The sample was random (from the population of US adults) and included 986 people, 400 of whom were women, and 586 were men. The mean score for women was 80.6, while the mean score for men was 77.6. 1. Is the difference in means test statistically significant at the 5% level? Assume the standard deviation for both men and women is 3.5. Show your work.
2. If the standard deviation for men is 1.4 and the standard deviation for women is 1.2, is the difference in means statistically significant at the 5% level? Show your work.
3. Why are large sample sizes usually better for making inferences about populations? Explain your answer (on the rest of this page).