Question

In the United States, Scholastic Aptitude Test (SAT) scores are used by universities when selecting students for admission. Private companies and high schools offer SAT preparatory courses to help students improve their scores. This has led some people to ask, "Do SAT preparatory classes effectively increase SAT scores?" The following study, cited in a major newspaper, claims that they do (but not by a substantial amount): "A new study . . . shows that [SAT preparatory] classes are effective in boosting scores-somewhat. 'Private classes increased scores an average of 60 points, while less specialised high school courses added 30 points,' said Claudia Buchmann, coauthor of the study and associate professor of sociology at Ohio State University [Source: Mehta, Seema. "Students Believe in the SAT." Los Angeles Times, March 1, 2008.] Imagine that a researcher would like to compare the effects on students' SAT scores of the following three types of preparation taking a private SAT preparatory class offered by ScoreExcel, a company offering exam reviews; taking a less specialised preparatory class offered by a local high school; and not taking any preparatory class Consider two statistical studies called Study A and Study B. In Study A, 180 high school year 12 students who had not taken the SAT were divided randomly into three groups of 60 students each. Students in the first group were assigned to take the preparatory class offered by ScoreExcel, those in the second group were assigned to take the preparatory class offered by the local high school, and those in the third group were not assigned to any preparatory class. At the end of the study, all of the students took the SAT, and their scores were recorded In Study B, samples of students who had taken the SAT were selected randomly from populations defined by the three different types of preparation: those taking the preparatory class offered by ScoreExcel, those taking the preparatory class offered by the local high school, and those not taking any preparatory class. Each sample consisted of 60 high school year 12 students, and their SAT scores were recorded

Answer 1

Let us solve one by one

a)

Here SAT score is dependent variable because it depends on the three types of preparation.

So SAT core is dependent variable and independent variable three types of study.

b)

Let us first understand the observational and experimental study

In an experiment study investigators apply treatments to experimental units.

In an observational study investigators observe subjects and measure variables of interest.

Study A is observational  study because We select sample who had taken SAT

Study B is experimental study because We select sample Who had not taken SAT.

Our claim is whether they differences among means of the population

Null Hypothesis H0: All population means are equal

Alternate Hypothesis: Ha: All population means are different

Perform ANOVA each population Response  variable has NORMAL distribution.

The variance of the dependent variable are EQUAL

And the observations are independent.

Satisfied the ANOVA design. observational study with RANDOM sampling.

F test statistics is the ratio of between treatment and within treatment.

When the null hypothesis is true grater than population variance.

So F-statistics not equal to 1

If null hypothesis is false then F test statistics is equal to 1.