# STATISTICS PROJECT: Hypothesis Testing

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