Question

A professor believes a greater proportion of females than males have enrolled in her class. Assuming there are an equal number of males and females in the student body, calculate chi-square, and evaluate her hypothesis based on the following data (n = 68). (6 points)

                  ____________________________________________________

                                             Males Enrolled                     Females Enrolled

                  ____________________________________________________

                  Observed                     22                                            46

                 

                  Expected_____________________________________________

Answer 1

Null hypothesis:- proportion of males and females is equal who have enrolled in her class

Alternate hypothesis: proportion of females is more than males who have enrolled in her class

we know that the expected Count = mean of observed values = (22+46)/2 = 68/2 = 34

Calculation for chi-square

setting the values, we get

Using the chi-square table, the corresponding p value for a chi square value of 8.47 with degree of freedom = 1 (because there is only one row and two columns)

we get p value = 0.0036

so, at 0.05 level of significance, we can reject the null hypothesis as the p value is significant.

Thus, we can conclude that the proportions of females is greater than proportion of males who have enrolled in her class.