STATISTICS PROJECT: Hypothesis Testing
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1)INTRODUCTION: Colleges often report a combined tuition and fees figure. According to the College Board, the average cost of tuition for the 2017–2018 school year was $34,740 at private colleges, $9,970 for state residents at public colleges, and$25,620 for outofstate residents attending public universities. Assume average yearly tuition cost of instate residents of 4yr. public college is (mu) “μ” >/= is $12070 per year. (Null Hypothesis))
 Research online (by going to at least 15 college websites) to find costs of different public colleges to test this claim. (Hint: use Facts & Figures e,g Rutgers University,NJ)
 Use the Ttest for a mean, since your sample is going to be less than 30 and an unknown population standard deviation.
Note: Make sure that your numbers only contain undergraduates and not graduates. As some of the websites were specific as to undergraduate or graduate and some probably contain both.
HYPOTHESIS: I think the average cost of tuition is lower than the assumed average stated.
Ho: μ (mu) >/= $12070.
H1: μ (mu) < $12070 (Claim)
DATA COLLECTION: Collect undergraduate students enrollment data from various college websites. Tabulate cost of tuition per year and the number of students enrolled. I already collected data for #1,an example and tubulated it as follows:
# 
College 
Tuition(Instate) 
Number of Students 
1 
Rutgers University–New Brunswick 
$11,999 
49,577 
2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 
 Find the lowest and the highest tuition. Calculate Range, Mean and Median for tuitions fees and enrollments.
HYPOTHESIS TESTING : (TTest for the Population Mean, When σ Is Unknown(TTest for a Mean)
Step 1: Identify the null and alternative hypotheses
Step 2: Set a value for the significance level, α = 0.05 is specified for this test
Step 3 : Determine the appropriate critical value
(Hint: Find the critical value at a=.025 and d.f. = 14, the critical value is –2.145.)– one tail
Step 4: Calculate the appropriate test statistic (i.e ttest statistic“t alpha” )
Step 5:Compare the ttest statistic with the critical tscore.Compute the sample test value.
Step 6: Make the decision to reject or not reject the null hypothesis.
Step 7: Summarize the results. (conclusion)
2)ChiSquared Independence Test
 Step 1: State the hypotheses and identify the claim. E.g. I claim that there is a correlation between the number of students at a college and the cost of tuition per year. Here is the data that is collected: (just an example to show the table – can change figuresif needed) Suppose α = 0.05 is chosen for this test
Cost of Tuition 
Number of Students 

10009999 
10000 19999 
20000 29999 
30000 – 39999 
40000 – 49999 
Total 

$3000 – $6000 

$6001 $9000 

$9001 – $12000 

$12001 – $15000 
1 

$15001 $18000 

Total 
Ho: The cost of tuition is independent of the number of students that attend the college. (x²=0)
H1: The cost of tuition is dependent on the number of students that attend the college. (claim : x²>0)
Step 2: Find the critical value
Step 3: Compute the test value. First find the expected value:
Step 4: Calculate the chisquare test statistic,
Step 5: Make the decision to reject or not to reject the null hypothesis.
Step 6: Summarize the results.
Anova Question (twoway ANOVA with replication)
3)The following table show the standardized math exam scores for a random sample of students for three states. The sample included an equal number of eightgraders and fourthgraders.
Tennessee 
Florida 
Arizona 

Eight Grade 
260 
292 
286 
255 
260 
274 

247 
287 
290 

277 
280 
269 

253 
275 
284 

260 
260 
297 

Fourth Grade 
275 
270 
286 
248 
283 
290 

250 
280 
295 

221 
270 
278 

236 
283 
258 

240 
290 
287 
 Perform twoway ANOVA (with replication) using α = 0.05 by defining Factor A as the state and Factor B as to whether the student was an eighthgrader or a fourthgrader.
 Test the effects that the state and the grade of the student have on the standardized math score
 State sources of variation within sample .
SS 
df 
MS 
F 
Pvalue 
F crit 
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