# College Tuition

Topics: Oregon, Northwest Commission on Colleges and Universities, Type I and type II errors Pages: 5 (1593 words) Published: November 10, 2012
STATISTICS PROJECT: Hypothesis Testing

See my comments in red. Scoring last page. INTRODUCTION My topic is the average tuition cost of a 4-yr. public college. Since I will soon be transferring to a 4-yr. college, I thought this topic would be perfect. "The College Board" says that the average tuition cost of college is \$5836 per year. I will be researching online the costs of different public colleges to test this claim. I will be using the T-test for a mean, since my sample is going to be less than 30 and an unknown population standard deviation. I will also use Chi-Square Test of Independence. HYPOTHESIS I think the average cost of tuition is lower than the average stated by “The College Board”. Ho: mu >/= \$5836. H1: mu< \$5836 (Claim) DATA ANALYSIS I collected my data from various college websites. I looked up the cost of tuition per year and the number of students enrolled. Here is what I came up with: College Central Washington University University of Washington Washington State University Western Washington University Evergreen State University Eastern Washington University Peninsula College University of Oregon Portland State University Oregon State University Southern Oregon University Eastern Oregon University Western Oregon University Tuition \$4392 \$5985 \$5888 \$4356 \$4590 \$5904 \$3639 \$6174 \$5208 \$5604 \$5233 \$4500 \$5763 Number of Students 10,200 25,469 18,432 13,000 4400 10,000 10,120 20,394 24,284 19,362 5000 3000 4500

University of Idaho Idaho State University

\$4410 \$4400

11,739 13,000

There weren’t really any large gaps or outliers in the data that I collected. There was a gap between 5,000 – 10,000 students. But the rest was mostly consistent. The lowest tuition was \$3639 from Peninsula College and the highest tuition was \$6174 from the University of Oregon. Some of the websites were hard to find the information I wanted, but I eventually found it. Some of the websites were specific as to undergraduate or graduate and some probably contain both. I should have done further research to make sure that my numbers only contain undergraduates and not graduates. So, that is one possible mistake in the data collection. You’ve explained your strengths and weaknesses in collection well.

HYPOTHESIS TESTING T-Test for a Mean Step 1: State the hypothesis and identify the claim. I claim that the average cost of college tuition is less than \$5836 per year as concluded from “The College Board”. At a=.025, can it be concluded that the average is less than \$5836 based on a sample of 15 colleges? H0: mu>/= \$5836 H1: mu0) Step 2: Find the critical value: The critical value is 14.449 since the degrees of freedom are (3-1)(4-1)=6. Step 3: Compute the test value. First we have to find the expected value: E1,1 = (6)(4)/15=1.6 E2,1 = (3)(4)/15=.8 E3,1 = (6)(4)/15=1.6 E1,2 = (6)(6)/15=2.4 E2,2 = (3)(6)/15=1.2 E3,2 = (6)(6)/15=2.4 E1,3 = (6)(3)/15=1.2 E2,3 = (3)(3)-15=.6 E3,3 = (6)(3)/15=1.2 E1,4 = (6)(2)/15=.8 E2,4 = (3)(2)/15=.4 E3,4 = (6)(2)/15=.8 I did some spot checking and it looks good. I’m going to trust you on chi-square. The completed table is shown: Cost of Tuition \$3500-4500 \$4501-5500 \$5501-6500 Total 3000-9,999 1 (1.6) 2 (.8) 1 (1.6) 4 10,000-16,999 5 (2.4) 0 (1.2) 1 (2.4) 6 Number of Students 17,000-23,999 0 (1.2) 0 (.6) 3 (1.2) 3 Total 24,000-30,999 0 (.8) 1 (.4) 1 (.8) 2

6 3 6 15

Then the test value is x² = ∑ (O-E)²/E = (1-1.6)²/1.6 + (5-2.4)²/2.4 + (0-1.2)²/1.2 + (0-.8)²/.8 + (2-.8)²/.8 + (01.2)²/1.2 + (0-.6)²/.6 + (1-.4)²/.4 + (1-1.6)²/1.6 + (1-2.4)²/2.4 + (3-1.2)²/1.2 + (1.8)²/.8 = 13.333 Step 4: Make the decision to reject or not to reject the null hypothesis. Do not reject the null hypothesis since 13.333 is less than 14.449. Step 5: Summarize the results. There is not enough evidence to support the claim that the cost of tuition is dependent on the number of students that attend the college.

SUMMARY My first hypothesis test about the tuition cost of 4-year universities being less than...