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.
- 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?
- The sample was randomly selected; therefore, it meets the assumption.
- The sample was randomly selected; therefore, it does not meet the assumption.
- The sample was not randomly selected; therefore, it meets the assumption.
- The sample was not randomly selected; therefore, it does not meet the assumption.
- State the Null and Research Hypotheses
- What is the null hypothesis?
- H0: r = 0
- H0: r = 1
- H0: r < 1
- H0: r ≠ 0
- What is the null hypothesis?
- What is the research hypothesis?
- H0: r = 0
- H0: r = 1
- H0: r < 1
- H0: r ≠ 0
- Determine the characteristics of the comparison distribution: r distribution with N-2 degrees of freedom
- MX =
- MY =
- SSX =
- SSY =
- SDX =
- SDY =
- Calculate the test statistic:
- r =
- How would you interpret the correlation coefficient?
- large, or strong, positive
- medium, or moderate positive
- small, or weak, positive
- large, or strong negative
- Make a decision based on critical value for the r distribution for 1-tailed test with an alpha level of 0.05.
- Fail to reject the null hypothesis because the sample correlation coefficient is greater than the critical value.
- Fail to reject the null hypothesis because the sample correlation coefficient is less than the critical value.
- Reject the null hypothesis because the sample correlation coefficient is greater than the critical value.
- Reject the null hypothesis because the sample correlation coefficient is less than the critical value.
- The population correlation coefficient r = .24, what type of error was committed?
- Type I error because we rejected a true null hypothesis.
- Type I error because we failed to reject a false null hypothesis.
- Type II error because we failed to reject a false null hypothesis.
- Type II error because we rejected a true null hypothesis.
- If this were a distribution of means, at what size would this sample need for the central limit theorem to apply?
- 15
- 20
- 25
- 30