Question

ith 34 degrees of freedom of 9.28 t statistics and standardized tests: On its Web site, the Princeton Review claims that students who have taken its course improve their Graduate Record Ex- amination (GRE) scores, on average, by 210 points (based on the old scoring system). (No other informa- tion is provided about this statistic.) Treating this aver- age gain as a population mean, a researcher wonders whether the far cheaper technique of practicing for the GRE on one's own would lead to a different aver- P 9.30tt dr sit th T age gain. She randomly selects five students from the pool of students at her university who plan to take the GRE.The students take a practice test before and after 2 months of self-study. They reported (fictional) gains of 160, 240, 340, 70, and 250 points. (Note that many experts suggest that the results from self-study are simi- lar to those from a structured course for students who t. have the self-discipline to study on their own. Regard- less of the format, preparation has been convincingly demonstrated to lead to increased scores, on average.) a. Using symbolic notation and formulas (where ap- propriate), determine the appropriate mean and standard error for the distribution to which we will compare this sample. Show all steps of your calculations b. Using symbolic notation and the formula, calculate the t statistic for this sample. c. As an interested consumer, what critical questions would you want to ask about the statistic reported by the Princeton Review? List at least three questions.

Answer 1

S = Elxi-x) mean. El) = t exit € 1060) (160-21212 +(240-212)2+(340-R12)+(70-21292 +(250-2122 5-1

101.8331 10 833) - Sfx = 45.541190 mean of x= x=2127 & standard error SE = 45.54 1190 b). t statistics 18-Mol (slun) 7- S. 4) E where, V as the sample mean llo is the population SE is the standard error where, s is standard deviation of the sample n is the sample size (212 -210) 45.541190 004391 c lists of questions on Princeton Review : i Why did you choose this school? ii) what majors are popular? iii) Are your classes lecture-based or discussion based? iu Are your professors good teachers?

Here the the sample points popkulation gains mean = 210 points are 160, 140, 340, To f 250 a) We have to determine the mean & Standard error. formulaes are in méant let suppose Here the reendom variable is x then mean of xa E(N) I J of sample pont where n is no Herl n-5 Here Standard enor ! Sk= where s is s.p. of sample.