I really need some help please save me :( College Tuition. We are interested in
ID: 3333869 • Letter: I
Question
I really need some help please save me :(
College Tuition.
We are interested in studying the differences between in-state tuition and out-of-state tuition at public and private four year colleges and universities in the US. A random sample of 25 private and 25 public institutions were collected and their tuition costs for the 2011-2012 academic year were recorded. The data is contained in the data set below.
a.)Determine the extent to which out-of-state tuition is more expensive than in-state tuition in the population of public schools.
i.) Do you want to construct a confidence interval or perform a hypothesis test to answer this question?
ii.) Do you need to use an independent two sample or matched pairs procedure?
iii.) Check assumptions and make transformations/adaptations if necessary.
iv.) State your final conclusion. Be careful to interpret your final result appropriate to the units in which it is expressed.
b.) Determine whether there is a difference in in-state tuition between private and public schools.
i.) Do you want to construct a confidence interval or perform a hypothesis test to answer this question?
ii.) Do you need to use an independent two sample or matched pairs procedure?
iii.) Check assumptions and make transformations/adaptations if necessary.
iv.) State your final conclusion.
c.) If there was a difference what is the extent of the difference in in-state tuition between private and public schools? Be careful when interpreting your result to express it in the appropriate units.
d.) Determine whether there is a difference in out-of-state tuition between private and public schools.
i.) Do you want to construct a confidence interval or perform a hypothesis test to answer this question?
ii.) Do you need to use an independent two sample or matched pairs procedure?
iii.) Check assumptions and make transformations/adaptations if necessary.
iv.) State your final conclusion.
Data Set:
Explanation / Answer
a.)Determine the extent to which out-of-state tuition is more expensive than in-state tuition in the population of public schools.
i.)
We first need to perform hypothesis testing. We can also construct confidence interval to check whether to reject or accept the null hypothesis.
ii.)
We would be using independent samples t-test because matched pairs samples is used when comparing the same group before and after some treatment.
iii.)
The assumptions for independent samples t-test are that samples are randomly and independently drawn, that populations are normally distributed and that population variances are unknown but assumed equal.
iv.)
H0: 1 - 2 = 0 i.e. (1 = 2)
H1: 1 - 2 >= 0 i.e. (1 2)
Assuming population variances are equal, we would have to calculate pooled-variance t-Test
Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)
= (25-1)*4500.4048^2+(25-1)*2633.68^2/24+24
= 13594956.85
tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)
=(16190.76-7152.36)-0/13594956.85 (1/25+1/25)
=9038.4/1042.87897
=8.6667775
tCRIT is +/- 2.01 and hence reject the null hypothesis since tSTAT > tCRIT
We have enough evidence to prove that out-of-state tuition is more expensive than in-state tuition in the population of public schools.
Confidence interval:-
(X1-X2)+-ta/2*Sp^2(1/n1+1/n2)
9038.4+-2.01*1042.87897
LCL=6942.21
UCL=11134.5867
Since 0 is not a part of the confidence interval, we reject the null hypothesis.
College Type OutOfState InState Albany State University Public 17048 5434 Appalachian State University Public 16487 5175 Central Connecticut State University Public 18679 8055 Christopher Newport University Public 19306 10084 City University of New York: Lehman College Public 12828 4978 City University of New York: Medgar Evers College Public 13352 5132 Colorado School of Mines Public 29139 14454 Delta State University Public 13688 5288 Fitchburg State University Public 13880 7800 Florida Atlantic University Public 18132 4794 Fort Lewis College Public 17616 5592 Indiana Universitiy East Public 16305 6069 Millersville University of Pennsylvania Public 16406 7700 Nevada State College Public 13401 3583 Northern Kentucky University Public 13896 7128 Oregon State University Public 20435 7115 Penn State Berks Public 19828 13250 Peru State College Public 4966 4966 Pittsburgh State University Public 13588 4848 South Dakota State University Public 7941 6444 University of Baltimore Public 17446 7494 University of Illinois: Springfield Public 19558 10408 University of Maine at Fort Kent Public 17535 7575 University of Texas at San Antonio Public 18173 8873 Virginia State University Public 15136 6570 Mean 16190.76 7152.36 Std Dev 4500.404827 2633.683255