Princeton Review We are examining an advertising flyer for the Princeton Review,

Question

Princeton Review We are examining an advertising flyer for the Princeton Review, a review course designed for high school students taking the SAT tests. The flyer claimed that the average score improvements for students who have taken the Princeton Review course is between 110 and 160 points. Are the claims made by the Princeton Review advertisers exaggerated? That is, is the average score improvement less than 110, the minimum claimed in the advertising flyer? A random sample of 100 students who took the Princeton Review course achieved an average score improvement of 107 points with a standard deviation of 13 points. a. State H_0 and H_a. b. Use the p-value approach to test the Princeton Review claim. At which significance levels can you reject H_0? Interpret the p-value in the context of this problem. c. Use the critical value approach to test the Princeton Review claim at alpha = 0.1. d. Calculate an appropriate confidence interval (two sided or one sided) and explain how it can be used to test the hypotheses. e. If you were a competitor of the Princeton Review, how would you state your conclusions to put your company in the best possible light? f. If you worked for the Princeton Review, how would you state your conclusions to protect your company's reputation?

Explanation / Answer

Given that,
population mean(u)=110
sample mean, x =107
standard deviation, s =13
number (n)=100
null, Ho: =110
alternate, H1: <110
level of significance, = 0.1
from standard normal table,left tailed t /2 =1.29
since our test is left-tailed
reject Ho, if to < -1.29
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =107-110/(13/sqrt(100))
to =-2.308
| to | =2.308
critical value
the value of |t | with n-1 = 99 d.f is 1.29
we got |to| =2.308 & | t | =1.29
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -2.3077 ) = 0.01155
hence value of p0.1 > 0.01155,here we reject Ho

ANSWERS
---------------
null, Ho: =110
alternate, H1: <110
test statistic: -2.308
critical value: -1.29
decision: reject Ho
p-value: 0.01155
we have enough evidence to support the claim

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