Question

A χ2 goodness-of-fit test was used to test the hypothesis that students at a local university select majors in the same proportions as other universities in the state. A chi-square test statistic of χ2=45.6 was calculated with a corresponding p -value of 0.005. Which of the following is correct?

Answer 1

Based on the information provided, we can make the following conclusions:

1. A chi-square goodness-of-fit test was used to test the hypothesis that students at a local university select majors in the same proportions as other universities in the state.
2. The calculated chi-square test statistic is χ2 = 45.6.
3. The corresponding p-value is 0.005.

Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis that the proportions of students selecting majors at the local university are the same as those at other universities in the state. This means that there is significant evidence to suggest that the proportions of students selecting majors at the local university are different from those at other universities in the state.

The chi-square test statistic of χ2 = 45.6 indicates a large deviation from the expected proportions, which further supports the rejection of the null hypothesis.

Therefore, the correct conclusion is that there is significant evidence to suggest that the proportions of students selecting majors at the local university are different from those at other universities in the state.