ACT Prep Course. ACT prep courses like to market that you canincrease your ACT score by taking their courses. Some statisticianswere curious how effective these courses really were. They decidedto investigate the truth of the claim by measuring the averagescore increase for a random sample of students selected to take anACT prep course. These students took the ACT twice, once before andonce after taking the course. The variable of interest was theincrease in scores between first and second attempts. NOTE: Thepopulation of interest is all students who took the ACT prepcourse.
(a) Identify µ in this scenario.
(Choose One)
• Average score of all people in the sample.
• True average increase in score of all people in thepopulation
. • True average score of all people in the population.
• Average increase in score by all people in the sample
. (b) In order to test the researcher’s claim, identify theappropriate: i. null hypothesis – H0 : ii. alternative hypotheses –Ha :
1 (c) Suppose that an average increase in score of 3 points (x =3) and standard deviation of s = 5.4 points were found in each ofthe following scenarios. Further, assume the difference in score isnormally distributed. For each case, compute the degrees of freedomand test statistic and assess the strength of evidence against thenull hypothesis. Round t-statistics to two decimals. i.
Scenario 1: a sample of size n = 9 A. t = with df = B. Thep-value corresponding to the correct test statistic is 0.06673.Based on this p-value, there is... • little to no evidence againstthe null hypothesis.
• borderline/weak evidence against the null hypothesis.
• moderate evidence against the null hypothesis. •
substantial/strong evidence against the null hypothesis.
• overwhelming evidence against the null hypothesis.
ii. Scenario 2: a sample of size n = 24 A. t = with df = B. Thep-value corresponding to the correct test statistic is 0.00611.Based on this p-value, there is... • little to no evidence againstthe null hypothesis.
• borderline/weak evidence against the null hypothesis.
• moderate evidence against the null hypothesis.
• substantial/strong evidence against the null hypothesis.
• overwhelming evidence against the null hypothesis.
iii. Scenario 3: a sample of size n = 444 A. t = with df = B.The p-value corresponding to the correct test statistic is<0.0001. Based on this p-value, there is...
• little to no evidence against the null hypothesis.
• borderline/weak evidence against the null hypothesis. •
moderate evidence against the null hypothesis. • s
substantial/strong evidence against the null hypothesis. •
overwhelming evidence against the null hypothesis.
