a 1993 nationwide survey by the national center for education statistics reports

Question

a 1993 nationwide survey by the national center for education statistics reports that 72% of all undergraduates work while enrolled in school. you decide to test whether this percent is different at your university. In your random sample of 100 students, 77 said they were currently working.

a) Give the null and alternative hypotheses for this study.

b) Cary out the significance test. Report the test statistic and P-value.

c) Does it appear that the percent of students working at your university is different at the a=0.05 level?

Explanation / Answer

a)
null hypothesis: 72% of undergraduates at your school work
alternative hypothesis: The proportion of undergraduates working at your school is different than 72%

b)
proportion of working students at your school: 0.77
Estimated standard deviation of measured proportion: (0.77 * (1-0.77) / 100) = 0.042
Test statistic = (0.77 - 0.72)/0.042 = 1.19
p-value (using t-distribution with 99 df): 0.1184

c)
No, the proportion of students at your school is not different from 72% at the a=0.05 level
since 0.1184 > 0.05

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