Question

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: LaTeX: H_0 H 0 : LaTeX: \mu=0 μ = 0 LaTeX: H_a H a : LaTeX: \mu>0 μ > 0 where LaTeX: \mu μ 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?

Answer 1

Level of significance = alpha = 0.05

Ho :- mu = 0

Vs Ha :- mu > 0 (claim)

Mu is the mean difference in SAT writing scores for all students

Test statistics = xbar /( sigma ÷√n) = 1.96

T critical = 1.68

T stat = 1.96 > t critical = 1.68

P value = 0.028 < 0.05 = alpha

We reject null hypothesis

There is sufficient evidence to conclude that SAT writing score after is greater than before the SAT score for all students .