# MATHEMATICS

Q20: The most appropriate null hypothesis (in words) 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.

Q21: The most appropriate null hypothesis (in symbols) would be

A. μSATprep = 1050

B. μSATprep = 1200

C. μSATprep ≤ 1050

D. μSATprep ≥ 1050

Q22: Set up the criteria for making a decision. That is, find the critical value using an

alpha = .01. (Make sure you are sign specific: + ; – ; or ± ) (Use your tables)

Summarize the data into the appropriate test statistic.

Steps:

Q23: What is the numeric value of your standard error?

Q24: What is the z-value or t-value you obtained (your test statistic)?

A. reject the null hypothesis

B. fail to reject the null hypothesis

Q26: 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.

Q27: Based on your evaluation of the null in Q25 and your conclusion is Q26, as a researcher

you would be more concerned with a

A. Type I statistical error

B. Type II statistical error

Calculate the 95% confidence interval.

Steps:

Q28: The mean you will use for this calculation is

A. 1050

B. 1200

Q29: What is the new critical value you will use for this calculation?

Q30: As you know, two values will be required to complete the following equation:

Q31: Which of the following is a more accurate interpretation of the confidence interval you

just computed?

A. We are 95% confident that the scores fall in the interval _____ to _____.

B. We are 95% confident that the average score on the SAT by the students who

took the prep course falls in the interval

C. We are 95% confident that the example above has correct values.

D. We are 95% confident that the difference in SAT scores between the students

who took the prep course and the students who did not falls in the interval

_____ to _____.The following 2 questions (Q32 to Q33) are based on the following situation:

The national average for the verbal section of the Graduate Record Exam (GRE) is 500

with a standard deviation of 100. A researcher uses a sampling distribution made up of samples of 100.

Q32: According to the Central Limit Theorem, what is the mean of the sampling distribution of

means?

A. 500

B. 100

C. 50

D. 10

Q33: According to the Central Limit Theorem, what is the standard error of the mean?

a. 500

b. 100

c. 50

d. 10

Q34: As you increase the number of subjects in your sample, the calculated

value of a t-test will

A. decrease

B. increase

C. remain the same

Q35: As you decrease the true distance between the null and alternative hypotheses

(μ1 – μ0), the likelihood of rejecting the null hypothesis

A. decreases

B. increases

C. remains the same

Q36: Keeping everything else the same, if you were to decrease your alpha level

from .05 to .01, the likelihood of rejecting the null hypothesis

A. decreases

B. increases

C. remains the same

The following 4 questions (Q37 to Q40) are either “True” or “False”

Q37: Predicting the characteristics of an entire group, after having measured a small group, is the major goal of inferential statistics.

Q38: The single-most critical component of deciding whether you are to conduct a t-test versus a z-test for hypothesis testing is whether there is a ‘µ’.

Q39: Degrees of freedom for a single sample t-test is/are ‘n-1’.

Q40: Degrees of freedom for a single sample z-test is/are ‘n-1’.

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