Question

2. ACT Prep Course. ACT prep courses like to market that by taking their course, you can increase your ACT score. Some statisticians were curious how effective these courses really were. They decided to investigate the truth of the claim by measuring the average score increase for a random sample of students selected to take an ACT prep course. These students took the ACT twice, once before and once after taking the course. The variable of interest was the increase in scores between first and second attempts. NOTE: The population of interest is all students who took the ACT prep course. (a) Identify u 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) In order to test the researcher's claim, identify the appropriate: i. null hypothesis – Ho : ii. alternative hypotheses – Ha:

Answer 1

Solution-a:

mu is for population here average increase in ACT for all members.

TRUE AVERAGE INCREASE IN SCORE OF ALL PEOPLE IN THE POPULATION

Solution-b:

Ho:$\mu 2-\mu 1=0$

Ha:$\mu 2-\mu 1>0$

mu1 is mean ACT score before prep course

and mu2 is mean score after taking prep course

Solution-c:

sceneraio-1

t=xbar-mu/s/sqrt/n)

=(2-0)/(3.4/sqrt(8)

t=1.664

df=n-1=8-1=7

df=7

p value in excel is

1- righ tail probbaility

=1-=T.DIST(1.664,7,TRUE)

=1-0.92997

p=0.07

p=0.07 given

p>0.05

Fail to reject null hypothesis

Accept Null hypothesis

MARK

Little to no evidence against null hypothesis