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Suppose we want to assess the effect of a one-day SAT prep class at a 5% level of significance. Scores on the SAT writing exam can range from 200 to 800. A random sample of 50 students takes the SAT writing test before and after a prep class. We test the hypotheses:

\[ H_0: \mu = 0 \]
\[ H_a: \mu > 0 \]

where \(\mu\) is the mean of the difference in SAT writing scores (after minus before) for all students who take the SAT prep class. The sample mean is 5 with a standard deviation of 18. Since the sample size is large, we are able to conduct the T-Test. The T-test statistic is approximately 1.96 with a P-value of approximately 0.028. What can we conclude?

A. The one-day SAT prep class is associated with statistically significant improvements in SAT writing performance.

B. Students taking a one-day SAT prep class performed significantly better on the SAT writing exam than students who did not take the class.

C. Students taking a one-day SAT prep class do not show statistically significant improvements in their SAT writing performance.

D. Scores only increased by 5 points, which is not significant on an exam where scores can range from 200 to 800.

E. The one-day SAT prep class produces statistically significant improvements in SAT writing performance.

Answer :

Answer: The one-day SAT prep class is associated with statistically significant improvements in SAT writing performance.

Step-by-step explanation: just took the quiz

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Rewritten by : Barada

The correct conclusion about the situation is, the one-day SAT prep class produces statistically significant improvements in SAT writing performance, which is option (e).

Given that:

It is assessing the performance of the students in the SAT writing exam before and after SAT prep class.

The hypothesis is:

H₀: μ = 0

H₁: μ > 0

This is a one-tailed test.

Here, the T-test is used.

Now, the significance level is, α = 0.05

p-value = 0.028

Since, the p-value, 0.028 is less than the significance level 0.05, the null hypothesis is rejected.

So, the mean of the difference in SAT scores is greater than 0.

That is, there is a significant effect in SAT exam by the prep class.

Hence, the correct conclusion is, The one-day SAT prep class produces statistically significant improvements in SAT writing performance, which is option (e).

Learn more about T-test here :

https://brainly.com/question/26462012

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