Smiling and Gender
In a 1997 study, people were observed for about 10 seconds in public places, such as malls and restaurants, to determine whether they smiled during the randomly chosen 10-second interval.
The table shows the results for comparing males and females. (Source: M. S. Chappell, Frequency of public smiling over the life span, Perceptual and Motor Skills, vol. 45: 474, 1997)
a. Find and compare the sample percentages of women who were smiling and men who were smiling.
b. Treat this as though it were a random sample, and test whether there are differences in the proportion of men and the proportion of women who smile. Use a significance level of 0.05.
c. Explain why there is such a small p-value even though there is such a small difference in sample percentages.