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 out-of-state residents attending public universities. Assume average yearly tuition cost of instate residents of 4-yr. public college is (mu) “μ” >/= is $12070 per year. (Null Hypothesis))
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Order Paper Now- 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 T-test 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(In-state) |
Number of Students |
1 |
Rutgers University–New Brunswick |
$11,999 |
49,577 |
2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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9 |
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10 |
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11 |
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12 |
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13 |
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14 |
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15 |
- Find the lowest and the highest tuition. Calculate Range, Mean and Median for tuitions fees and enrollments.
HYPOTHESIS TESTING : (T-Test for the Population Mean, When σ Is Unknown(T-Test 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 t-test statistic-“t alpha” )
Step 5:Compare the t-test statistic with the critical t-score.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)Chi-Squared 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 |
|||||
1000-9999 |
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 chi-square test statistic,
Step 5: Make the decision to reject or not to reject the null hypothesis.
Step 6: Summarize the results.
Anova Question (two-way 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 eight-graders and fourth-graders.
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 two-way ANOVA (with replication) using α = 0.05 by defining Factor A as the state and Factor B as to whether the student was an eighth-grader or a fourth-grader.
- 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 |
P-value |
F crit |
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