Keiser University Statistics Worksheet

STATISTICS PROJECT: Hypothesis TestingSee 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 Tuition 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 $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 the average was correct. The average as stated by “The College Board”
said that the tuition was $5836 per year. I thought that was a little high. The
average tuition of the fifteen colleges that I researched was $5069.73. Maybe if I
would have researched colleges all around the country instead of just our
surrounding states I would have come up with different numbers. Another thing
that may have caused this test to be a little off was that when I was collecting
data, some of the costs of tuition may include other fees and some may not.
When I looked them up, some fees were listed separately and some were not.
This could have lead to a Type I error where the null hypothesis was true and it
was rejected. Good note on the possibility of a Type I error.
My second hypothesis test about whether the cost of tuition is dependant on the
number of students that attend the college was rejected. I thought that the fewer
the students that attend a specific college, that tuition would be cheaper, but that
wasn’t the case. One main problem I can see with colleting my data is that on
the college websites for the number of students, some said “over” or
“approximately”. So, these weren’t the exact numbers of students enrolled.
Also, as stated earlier, some of the students could be undergraduates or
graduates. Some of the websites didn’t list them separately. Tuition is higher for
graduates, so they should not have been included in this study and it would have
thrown off the number of students. So, these may have affected the outcome a
little, but I don’t’ think enough for it to change the hypothesis. Small differences,
including rounding, can really throw off your test value in this type of test.
It would have also been interesting to test to see whether the tuition is higher in
urban areas where more people live verses rural areas where there are not as
many people. I would be inclined to say that this is true, but it would need to be
tested further to say for sure. It would also be interesting to do this same testing
for private colleges to see if they have the same results. I thought this was fun to
come up with our own hypothesis and try to prove ourselves right or wrong using
what we have learned all quarter. It was a good test of our skills and it made me
get a better understanding of how the formulas really work rather than just doing
the homework examples in the book.
Excellent summary/critique and project overall. I’ve been teaching this class for
over 8 years and your project is one of the best. Can I please use this as a
sample?
Grading Rubric
Statistics Project, Spring 2007
Objective Met (C, B-) Exceeded (B, B+)
Outstanding (A-, A)
Score
Hypothesis and
Proposal
10 points
Statement of hypothesis in
Statement of hypothesis in words and symbols.
words or symbols, type of Description of test you’ll
test you plan to use.
use and how you plan to
implement it.
Statement of hypothesis in
words and symbols,
including motivation. Type
of hypothesis test and plans
for implementation.
10
Written Project:
Data Analysis
15 points
Brief description the data Description and
set including outliers, gaps, interpretation of data set
and other observations.
(what and why).
Description and
interpretation of data set.
Discussion of potential
problems including how data
could be improved.
15
Written Project:
Hypothesis Testing Conduct a mathematically
accurate hypothesis test.
and Confidence
Intervals 30 points
Conduct two (or more)
Conduct two
mathematically correct
mathematically correct
hypothesis tests that allow
hypothesis tests or one test
you to draw meaningful
and one confidence interval
conclusions.
Explain outcome of
hypothesis testing, discuss
Written Project:
possibility of Type I or
Summary and SelfRe-iterate outcome of
Type II errors. Explore
Critique
hypothesis testing. Identify
25 points
areas of strength and
areas of strength and
weakness by making
weakness.
suggestions for
improvement and
proposing further research.
Overall Subjective
Component
10 points
Draft and Edits
10 points
29
Interpret outcome of
hypothesis testing and
possibility of Type I or II
errors. Explain errors. Draw
connections between
hypothesis tests, data
collection. Discuss areas of
strength and weakness.
25
Project is accurate, creative,
and well-presented.
Hypothesis testing done at
mastery level with
meaningful connections
throughout and a thorough
summary and
recommendation (I was
“wowed”)
10
Project is mathematically
and grammatically correct.
Displays adequate
understanding of
hypothesis testing.
Project is accurate,
interesting, and wellpresented. Displays
mastery of hypothesis
testing.
Draft in by due date = 5
points
Draft submitted and constructive review of one other
classmate’s done by due dates = 10 points
Overall Score
10
99
Written by Angela Redmon. Last updated 07/12/06.
Figure 4. Men who took medication or talked to a mental health professional, among men aged 18 and over who felt
anxious or depressed every day, by age and race and ethnicity: United States, 2010-2013
60
Percent
30
30
40
50
20
20
10
0
All races and ethnicities
39.2
145.4
18-44
226.4
Non-Hispanic white
Non-Hispanic black and Hispanic
46.4
42.3
41.3
45 and over
Age group (years)
‘Significantly different from non-Hispanic black and Hispanic men in the same age group.
2Significantly different from men aged 45 and over in the same race and ethnicity group.
SOURCE: CDC/NCHS, National Health Interview Survey, 2010-2013.