RMS I Spring 2022 Final Exam
To investigate the association between extraversion and musical preference, Peter Rentfrow and Sam Gosling (2003) asked a set of undergraduate students about their favorite types of music, using a self-report questionnaire they called the STOMP (short test of music preferences). They also measured the same students’ personality traits using a self-report measure that assessed people’s extraversion, agreeableness, conscientiousness, and other traits.
Liking for upbeat, conventional music (X) |
Extraversion score from personality questionnaire (Y) |
4.00 |
3.75 |
3.00 |
2.75 |
2.43 |
5.00 |
3.57 |
4.00 |
4.29 |
5.75 |
Calculate the correlation coefficient and conduct hypothesis testing to determine whether the correlation is statistically significant.
1. Identify the populations, comparison distribution and assumptions: We are sampling from a population of undergraduate students. Our comparison distribution is a distribution of correlations. Assuming the distribution is approximately normal, which statement is true about the remaining assumption?
a. The sample was randomly selected; therefore, it meets the assumption.
b. The sample was randomly selected; therefore, it does not meet the assumption.
c. The sample was not randomly selected; therefore, it meets the assumption.
d. The sample was not randomly selected; therefore, it does not meet the assumption.
2. State the Null and Research Hypotheses
i. What is the null hypothesis?
a. H0: r = 0
b. H0: r = 1
c. H0: r < 1
d. H0: r ≠ 0
ii. What is the research hypothesis?
a. H0: r = 0
b. H0: r = 1
c. H0: r < 1
d. H0: r ≠ 0
3. Determine the characteristics of the comparison distribution: r distribution with N-2 degrees of freedom
i. MX =
ii. MY =
iii. SSX =
iv. SSY =
v. SDX =
vi. SDY =
4. Calculate the test statistic:
i. r =
ii. How would you interpret the correlation coefficient?
a. large, or strong, positive
b. medium, or moderate positive
c. small, or weak, positive
d. large, or strong negative
5. Make a decision based on critical value for the r distribution for 1-tailed test with an alpha level of 0.05.
a. Fail to reject the null hypothesis because the sample correlation coefficient is greater than the critical value.
b. Fail to reject the null hypothesis because the sample correlation coefficient is less than the critical value.
c. Reject the null hypothesis because the sample correlation coefficient is greater than the critical value.
d. Reject the null hypothesis because the sample correlation coefficient is less than the critical value.
6. The population correlation coefficient r = .24, what type of error was committed?
a. Type I error because we rejected a true null hypothesis.
b. Type I error because we failed to reject a false null hypothesis.
c. Type II error because we failed to reject a false null hypothesis.
d. Type II error because we rejected a true null hypothesis.
7. If this were a distribution of means, at what size would this sample need for the central limit theorem to apply?
a. 15
b. 20
c. 25
d. 30