Question

: Are freshmen psychology majors less likely to change their major before they graduate compared to freshmen business majors? 475 of the 688 freshmen psychology majors from a recent study changed their major before they graduated and 489 of the 691 freshmen business majors changed their major before they graduated. What can be concluded at the a = 0.01 level of significance?: Are freshmen psychology majors less likely to change their major before they graduate compared to freshmen business majors? 475 of the 688 freshmen psychology majors from a recent study changed their major before they graduated and 489 of the 691 freshmen business majors changed their major before they graduated. What can be concluded at the a = 0.01 level of significance?v

Answer 1

Using a hypothesis test for two proportions, we can compare the likelihood of psychology and business majors changing their majors. The analysis at the 0.01 significance level will reveal if there's enough evidence to support the claim that psychology majors are less likely to change majors compared to business majors.

Step-by-step explanation:

To determine whether freshmen psychology majors are less likely to change their major compared to freshmen business majors, we can apply a hypothesis test for the difference between two proportions at the 0.01 significance level. The number of psychology majors who changed their major is 475 out of 688, and the number of business majors who changed is 489 out of 691.

First, we will define the null hypothesis (H0) as there being no difference between the two proportions, and the alternative hypothesis (Ha) as the proportion of psychology majors who change their major being less than the proportion of business majors who do so.

To carry out the test, we compute the test statistic, which follows a standard normal distribution under H0. The standard normal test statistic (z) is calculated using the formula for the difference between two proportions. If the calculated z-value is less than the critical z-value at the 0.01 significance level, we reject the null hypothesis; otherwise, we fail to reject it.

If we calculate and find the p-value to be less than 0.01, we reject the null hypothesis, concluding that there is sufficient evidence at the 0.01 level to say that psychology majors are less likely to change their major. If not, we do not have sufficient evidence to suggest a difference.