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))

  • 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

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 : (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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