SAT Prep Course. SAT prep courses like to market that by taking their course, yo
ID: 3216712 • Letter: S
Question
SAT Prep Course. SAT prep courses like to market that by taking their course, you can increase your SAT score. Some statisticians were curious how effective these courses really were. They decided to investigate the truth of the claim.
(a) Identify µ in this scenario. (Choose One)
• Average increase in score by all people in the sample.
• True average increase in score of all people in the population.
• True average score of all people in the population.
• Average score of all people in the sample.
(b) Identify the appropriate null and the alternative hypotheses to test the researchers’ claim.
H0 :_____________ Ha :________________
(c) Suppose that an average increase in score of 5 points (x = 5) and standard deviation of s = 25 points were found in each of the following scenarios. Further, assume difference in score is normally distributed. For each case, compute the test statistic, find the approximate p-value and make a decision about the null hypothesis using an = 0.05 level of significance. Round t-statistics to two decimals.
i. Scenario 1: a sample of size n = 10
A. t =_____________ and df =______________
B. The p-value corresponding to the correct test statistic is 0.271. This p-value suggests ____________ against the null hypothesis. (Choose One)
• Little or no evidence
• Weak evidence
• Moderately strong evidence
• Strong evidence
• Extremely strong evidence
C. Decision:
• Reject the null hypothesis because the p-value .
• Reject the null hypothesis because the p-value > .
• Fail to reject the null hypothesis because the p-value .
• Fail to reject the null hypothesis because the p-value > . ii.
Scenario 2: a sample of size n = 80
A. t = _____________ and df = ____________
B. The p-value corresponding to the correct test statistic is 0.039. This p-value suggests against the null hypothesis. (Choose One)
• Little or no evidence
• Weak evidence
• Moderately strong evidence
• Strong evidence
• Extremely strong evidence
C. Decision:
• Reject the null hypothesis because the p-value .
• Reject the null hypothesis because the p-value > .
• Fail to reject the null hypothesis because the p-value .
• Fail to reject the null hypothesis because the p-value > .
iii. Scenario 3: a sample of size n = 800
A. t =_________ and df =_________
B. The p-value corresponding to the correct test statistic is 0.000000011. This p-value suggests __________ against the null hypothesis. (Choose One)
• Little or no evidence
•Weak evidence
• Moderately strong evidence
• Strong evidence
• Extremely strong evidence
C. Decision:
• Reject the null hypothesis because the p-value .
• Reject the null hypothesis because the p-value > .
• Fail to reject the null hypothesis because the p-value .
• Fail to reject the null hypothesis because the p-value > .
Explanation / Answer
ANSWERS:
a) True average increase in score of all people in the population
b) Ho: population mean <= 0; Ha: population mean>0
c) n= 10;sample mean = 5; s =25
standard error = s/sqrt(n) = 25/sqrt(10) = 7.9057
A) t-statistic = (sample mean-population mean) / s.e.
=(5-0) / 7.9057 = 0.63
t-statistic = 0.63
d.f. = (n-1) = 10-1 = 9
B) The p-value corresponding to the correct test statistic is 0.271. This p-value suggests Little or no evidence against the null hypothesis.
C. Decision: Fail to reject the null hypothesis because the p-value >
III) n = 800; s.e. = s/sqrt(n) = 25/sqrt(800) = 0.8839
A) t-statistic = (sample mean-population mean) / s.e.
= (5-0)/0.8839
t-statistic = 5.66; df=800-1=799
B) The p-value corresponding to the correct test statistic is 0.000000011. This p-value suggests Extremely strong evidence against the null hypothesis
C. Decision:Reject the null hypothesis because the p-value
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