The U.S. Department of Education reports that 40% of full-time college students are employed while attending college. (Data extracted from National Center for Education Statistics, The Condition of Education 2012, nces.ed.gov/ pubs2012/2012045.pdf.) A recent survey of 60 full-time students at a university found that 25 were employed.
a. Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to determine whether the proportion of full-time students at the university is different from the national norm of 0.40.
b. Assume that the study found that 32 of the 60 full-time students were employed and repeat (a). Are the conclusions the same?