Reference no: EM133634529

Exercise 5: Sociologists have conducted much interesting research on gender stereotypes in American society. A curious aspect of stereotypes is that people tend to perceive differences between groups to be greater than they actually are. This suggests, for example, that when asked about the heights of men and women, survey respondents would tend to perceive men to be taller than women. Suppose you wanted to test this notion that individuals perceive a greater height difference between men and women than exists in the population. In the population, men, on average, are 5 inches taller than women. So the true population difference between men and women is 5 inches. You obtain a random sample of 400 individuals. For each respondent you record his or her perceptions of the difference between male and female heights. In your sample, you find that the mean difference in perceived heights is 6 inches. So respondents perceive that men are 6 inches taller than women. The sample standard deviation is 4 inches. A. Calculate the standard error of the sample mean. B. Using the ±2 shortcut, calculate the 95 percent confidence interval. C. If the true gender difference is 5 inches, can you infer from your sample that individuals perceive a greater difference than actually exists? Explain.