Question

3You also have been asked to determine at both the 5% and 10% levels of significance whether the proportion of the population of universities that offers more than 50% of their student body some sort of financial aid is different from 40%. You select a random sample of universities from the population. The sample data concerning whether the university offers more than 50% of its students some form of financial aid is shown below. Answer the question posed above at each of the stated levels of significance based upon the sample data given in appendix two. If you arrive at different results for the two different parts of this problem, provide a reason for that difference. Appendix Two: University offers more than 50% of its students financial aid? (Y = yes, N = no)

Y         N         Y         Y         N         Y         N         N         N         Y         Y        

N         N         Y         Y         Y         N         N         Y         N         N         N        

N         Y         Y         Y         N         Y         Y         N         Y         N         Y

Y         N         Y         Y         Y         Y         Y         N         N         N         Y

N         Y         N         N         N         N         Y         Y         N         Y         Y

Y         Y         Y         N         Y         Y         Y         Y         N         N         Y

Answer 1

We want to know whether the more than 50% universities offer some sort of financial aid to the students. A random sample is given. This a test fro true population proportion.

: p = 40%. 40% universities offer more than 50% financial aid.

: p 40%. 40% universities do not offer more than 50% financial aid.

Test Statistic =

Where = No. of yeses / n

= 37 / 66 = 0.561

Null proportion = = 40%

Test Stat =

Test Stat = 2.6289

We use a z-test for proportion. It is one tailed since we are only checking if it is more than or not.

Critical value = ..................We use normal percentage tables

Level of significance	5%	10%
Critical value	1.6449	1.2816
comparison	Test Stat > Critical V	Test Stat > Critical V
Decision	Reject null hypothesis	Reject null hypothesis
Conclusion	Significanclty at 5% not 40% universities offer more than 50% financial aid.	Significanclty at 10%, not 40% universities offer more than 50% financial aid.