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))
- 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:
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#
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College
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Tuition(In-state)
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Number of Students
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1
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Rutgers University–New Brunswick
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$11,999
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49,577
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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
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- 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
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Cost of Tuition
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Number of Students
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1000-9999
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10000 -19999
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20000 -29999
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30000 – 39999
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40000 – 49999
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Total
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$3000 – $6000
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$6001 -$9000
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$9001 – $12000
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$12001 – $15000
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1
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$15001 -$18000
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Total
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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.
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Tennessee
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Florida
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Arizona
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Eight Grade
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260
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292
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286
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255
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260
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274
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247
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287
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290
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277
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280
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269
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253
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275
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284
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260
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260
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297
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Fourth Grade
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275
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270
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286
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248
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283
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290
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250
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280
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295
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221
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270
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278
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236
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283
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258
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240
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290
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287
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- 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 .
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SS
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df
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MS
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F
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P-value
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F crit
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