Question

Are freshmen psychology majors just as likely to change their major before they graduate compared to freshmen business majors? 339 of the 611 freshmen psychology majors from a recent study changed their major before they graduated and 369 of the 732 freshmen business majors changed their major before they graduated. What can be concluded at the  = 0.10 level of significance?

For this study, we should use Select an answer z-test for a population proportion t-test for a population mean t-test for the difference between two independent population means t-test for the difference between two dependent population means z-test for the difference between two population proportions

1. The null and alternative hypotheses would be:   
2.   

   Select an answer p1 μ1  Select an answer < ≠ > =  Select an answer p2 μ2  (please enter a decimal)   

   Select an answer μ1 p1  Select an answer > ≠ = <  Select an answer μ2 p2  (Please enter a decimal)

2. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
3. The p-value =  (Please show your answer to 4 decimal places.)
4. The p-value is ? > ≤  
5. Based on this, we should Select an answer fail to reject accept reject  the null hypothesis.
6. Thus, the final conclusion is that ...
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population proportion of freshmen psychology majors who change their major is different from the population proportion of freshmen business majors who change their major.
   • The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population proportion of freshmen psychology majors who change their major is the same as the population proportion of freshmen business majors who change their major.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the proportion of the 611 freshmen psychology majors who changed their major is different from the proportion of the 732 freshmen business majors who change their major.
   • The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population proportion of freshmen psychology majors who change their major is different from the population proportion of freshmen business majors who change their major.

Answer 1

Let denote the proportions of people who changed their major before they graduated among psychology majors freshmen and business majors freshmen respectively.

For this study, we should use z-test for the difference between two population proportions

e) The results are statistically significant at α = 0.10, so there is sufficient evidence to conclude that the population proportion of freshmen psychology majors who change their major is different from the population proportion of freshmen business majors who change their major.