Question

Dr. Rulet is an expert in addictive behaviors. One day it occurred to her that perhaps mathematic efficiency is related to gambling addiction. Therefore, she instructed her lab to test a handful of known gambling-addicted individuals on both the SAT mathematics section and the Gambling-related Addiction Behavior (GAB) scale. The data is summarized below:

SAT Math	GAB Score
500	30
636	38
588	31
670	40
720	42
600	44
590	31
684	49

With the above data, answer the following:

1. When Dr. Rulet thought about this possible relationship between mathematic efficiency and gambling addiction, she reasoned that those who are good at mathematics might be more inclined to use their ability to gamble (and thus be more addicted). She therefore hypothesized that the participants’ GAB score would increase as SAT mathematics scores increased. State the appropriate alternative and null hypotheses using the statistical notation for stating mathematical relationships.

2. What is the strength and direction of the relationship between the SAT mathematic and GAB scores?

3. Assuming an alpha level of 0.05, provide the critical and obtained values for this hypothesis test.

4. Assuming an alpha level of 0.05, make a decision as to whether the result of the hypothesis test is significant or insignificant, as well as whether you should reject or fail to reject the null hypothesis, being sure to explain why. Also, interpret the results of the hypothesis test in everyday language (i.e., is there a reliable relationship between SAT mathematic and GAB scores?).

Answer 1

Question 1

Null hypothesis: H₀: There is no any correlation or linear relationship exists between the two variables SAT Math and GAB Score.

Alternative hypothesis: H_a: There is a positive correlation or linear relationship exists between the two variables SAT Math and GAB scores.

H₀: ρ = 0 versus H_a: ρ > 0

Question 2

From given data, we have

Correlation coefficient = r = 0.734663

This means there is a moderate strong positive linear relationship exists between given two variables.

Question 3

We are given

n = 8

df = n- 2 = 8 – 2 = 6

α = 0.05

Critical value = 2.4469

Test statistic = t = r*sqrt(n – 2)/sqrt(1 – r^2)

t = 0.734663*sqrt(8 - 2)/sqrt(1 - 0.734663^2)

t = 2.652512

Question 4

From above part, test statistic t is greater than the critical value, so we reject the null hypothesis.

There is sufficient evidence to conclude that there is a positive correlation or linear relationship exists between the two variables SAT Math and GAB scores.