SAT
a New SAT Preparation Program Claims That Students Will

question 63

Essay

SAT
A new SAT preparation program claims that students will improve their verbal scores with a practice test after one month on the program.To validate their claim,they recorded the starting and practice verbal SAT scores of 12 individuals after a one-month period.The results are shown in the following table.
$$\begin{array} { | c | c | } \hline \text { Starting SAT Score } & \text { Practice SAT Score } \\\hline 450 & 460 \\\hline 390 & 390 \\\hline 425 & 430 \\\hline 510 & 500 \\\hline 520 & 525 \\\hline 440 & 420 \\\hline 550 & 570 \\\hline 610 & 625 \\\hline 490 & 510 \\\hline 475 & 485 \\\hline 535 & 540 \\\hline 500 & 500 \\\hline\end{array}$$
-Use $\alpha$ = 0.01.State the decision rule in terms of the critical value.

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Definitions:

Difference-In-Differences

Difference-in-differences is a method for identifying causality by looking at the way in which the average change over time in the outcome variable is compared to the average change in a control group.

Causality

The relationship between cause and effect, often established through correlation and experimentation.

Outcome Variable

The variable in a study or experiment that is measured to assess the effect of the treatment or intervention.

Intention To Treat

A principle in clinical trials that includes all participants in the groups to which they were originally assigned, regardless of whether they completed the treatment or not, to ensure that the trial results are unbiased and reflect the real-world effectiveness of the treatment.