A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section.The population standard deviation of the SAT is known to be 100.Use an alpha level of .05 when answering the following questions.What conclusions can be made,based on this test statistic?
A)The score of the students who took the Kaplan course was better than the national mean only because of sampling error.
B)The Kaplan course helped the students score statistically significantly higher than the national mean.
C)The Kaplan course helped the students score statistically significantly lower than the national mean.
D)none of these conclusions can be made

Question

Quizplus · Accepted Answer

We need to conduct a one-sample t-test using the given information. The null hypothesis is that the mean score of the students who took the Kaplan course is not significantly different from the national mean of 500. The alternative hypothesis is that the mean score of the students who took the Kaplan course is significantly higher than the national mean of 500.

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
t = (sample mean - 500) / (100 / sqrt(200))
t = (sample mean - 500) / 7.07

We can use a t-distribution table with degrees of freedom = 199 and an alpha level of .05 to find the critical t-value. The critical t-value is 1.96.

If the calculated t-value is greater than the critical t-value, we reject the null hypothesis and conclude that there is a significant difference between the sample mean and the population mean. If the calculated t-value is less than or equal to the critical t-value, we fail to reject the null hypothesis.

Here, we calculate the t-value as follows:

t = (sample mean - 500) / 7.07 = (520 - 500) / 7.07 = 2.83

Since 2.83 is greater than 1.96, we reject the null hypothesis and conclude that the Kaplan course helped the students score statistically significantly higher than the national mean. Therefore, the best choice is B.

A Group of 200 Students Takes the Kaplan Course in Hopes