Answer to Question #12605 in Statistics and Probability for Theresa Rice

Question

You notice at the gym that it appears more women tend to work out together, whereas more men tend to work out alone. To determine whether this difference is significant, you collect data on the workout preferences for a sample of men and women at your gym. The data follows.
Males Females
Together 5 8
Alone 7 6

What statistical test should be used to analyze the data?
Identify H0 and Ha for this study
Conduct the appropriate analysis.
Should H0 be rejected? What should the researcher conclude?

Answer 1

This test is particular case of chi-square test and is called exact Fisher test.
H0 is : there is no dependence on sex, whether the particular human tends to work alone or together.
H1 is: there is dependence on sex, whether the particular human tends to work alone or together.
The two-tailed P value equals 0,6951 > 0,05 . The association between rows (groups) and columns (outcomes) is considered to be not statistically significant. Hence we have to choose the H1 hypothesis and to reject H0.
The conclusion is: there is no difference between men and women in their tending to work together or alone in the gym.