# Question: Are women happier than men A StatCrunch survey asked respondents

Are women happier than men? A StatCrunch survey asked respondents to select a number from 1 (lowest) to 100 (highest) to measure their level of happiness. The sample mean for the 297 females was 71.15, and the sample mean for the 380 males was 67.08. To determine whether the population mean for women was higher than the population mean for men, we used a randomization test.

a. The histogram shows the results of 1000 randomizations of the data.

In each randomization, 297 observations from the combined data were randomly marked "female," and the rest were randomly marked "male." We calculated the mean difference in happiness between these two randomly determined groups. Note that the distribution is centered at about 0, just as it should be, since we carried out the randomiza tion in such a way that the null hypothesis is true. The red line shows the observed sample mean difference in happiness for the women minus the happiness for the men. From the graph, does it look like the observed mean difference is unusual for this data set? Explain.

b. The software output estimates the probability of having an observed difference of 4.07 or more. (See the output column labeled "Proportion = 7 Observed"). Where does the value of 4.07 (or 4.0718) come from?

c. State the p-value.

d. Using a significance level of 0.05, can we reject the null hypothesis that the means are equal and so conclude that women StatCrunch users tend to be happier than men StatCrunch users? (Assume the sample was randomly selected from the population of all StatCrunch users.)

a. The histogram shows the results of 1000 randomizations of the data.

In each randomization, 297 observations from the combined data were randomly marked "female," and the rest were randomly marked "male." We calculated the mean difference in happiness between these two randomly determined groups. Note that the distribution is centered at about 0, just as it should be, since we carried out the randomiza tion in such a way that the null hypothesis is true. The red line shows the observed sample mean difference in happiness for the women minus the happiness for the men. From the graph, does it look like the observed mean difference is unusual for this data set? Explain.

b. The software output estimates the probability of having an observed difference of 4.07 or more. (See the output column labeled "Proportion = 7 Observed"). Where does the value of 4.07 (or 4.0718) come from?

c. State the p-value.

d. Using a significance level of 0.05, can we reject the null hypothesis that the means are equal and so conclude that women StatCrunch users tend to be happier than men StatCrunch users? (Assume the sample was randomly selected from the population of all StatCrunch users.)

**View Solution:**## Answer to relevant Questions

In Exercise 13.24 you compared credit card debts for college men and women using the Mann-Whitney test to compare medians. We'll use the same data again, but this time you will apply a randomization test to determine whether ...Many people believe that healthy people typically have a body temperature of 98.6°F. We took a random sample of 10 people and found the following temperatures: 98.4, 98.8, 98.7, 98.7, 98.6, 97.2, 98.4, 98.0, 98.3, and 98.0 ...Find the difference in number of texts received and the number sent for females. Do the same for males. Then determine whether the differences are significantly different at the 0.05 level using the two-sample t-test. Do older college students tend to weigh more than younger college students? Our data are ages and weights for a random sample of 76 college students. A scatterplot (not shown here) shows that the association between age and ...Figure A contains the selling price and area (in square feet) of 81 recently sold homes in a region where a buyer wants to purchase a home. a. Use the equation to estimate the price of a home with 2500 square feet. b. The ...Post your question