Question

Are freshmen psychology majors less likely to change their major before they graduate than freshmen business majors? 357 of the 792 freshmen psychology majors from a recent study changed their major before they graduated and 284 of the 563 freshmen business majors changed their major before they graduated. What can be concluded at the 0.05 level of significance?

Answer 1

To identify if freshman psychology majors or business majors are more likely to change their major before graduation, a hypothesis test for two proportions is conducted at the 0.05 level of significance using a two-proportion z-test.

Step-by-step explanation:

To determine whether freshmen psychology majors are less likely to change their major before they graduate compared to freshmen business majors, we must conduct a hypothesis test for two proportions at the 0.05 level of significance.

The null hypothesis (H0) is that there is no difference in the proportion of students who change majors between the two groups, while the alternative hypothesis (H1) is that there is a difference.

Firstly, we must calculate the sample proportions of students who changed majors for each group. For psychology majors:

357 out of 792 changed their major, so the sample proportion is 357/792. For business majors:

284 out of 563 changed their major, so the sample proportion is 284/563.

Next, we perform a two-proportion z-test to compare the proportions of students changing majors between psychology and business. We calculate the z-statistic, compare it with the critical value for a two-tailed test at a 5% significance level, and determine whether to reject the null hypothesis based on this comparison.