Question

A researcher wants to determine whether high school students who attend an SAT preparation course score significantly different on the SAT than students who do not attend the preparation course. For those who do not attend the course, the population mean is 1050 (? = 1050). The 16 students who attend the preparation course average 1200on the SAT, with a sample standard deviation of 100. On the basis of these data, can the researcher conclude that the preparation course has a significant difference on SAT scores? Set alpha equal to .01.

Summarize the data into the appropriate test statistic. Steps:

Q6: What is the numeric value of your standard error?

Q7: What is the z-value or t-value you obtained (your test statistic)?

Q8: Based on your results would you

A. reject the null hypothesis

B. fail to reject the null hypothesis

Q9: The best conclusion for this example would be

A. There is no statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.

B. There is a statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.

C. The students who took the SAT prep course did not score significantly higher on the SAT when compared to the general population of students who did not take the SAT prep course.

D. The students who took the SAT prep course did score significantly higher on the SAT when compared to the general population of students who did not take the SAT prep course.

Q10: Based on your evaluation of the null in Q5 and your conclusion is Q6, as a researcher you would be more concerned with a

A. Type I statistical error

B. Type II statistical error

Answer 1

6) SE = s / √n = 100/√16 = 25

7)The test statistic is t = x(bar) - mu / SE = 1200 - 1050 / 25 = 6

The critical value is t_15,.01 = 2.9467

8)Since t value is greater than t_cric , we reject the null hypothesis.

9) The final conclusion is B. There is a statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.

10)Since the possible error here is accepting the false null hypothesis , the error is type II (B)