Question
In: Statistics and Probability
15. To measure the relationship between anxiety level and test performance, a psychologist obtains a sample...
15. To measure the relationship between anxiety level and test performance, a psychologist obtains a sample of n=7 college students from an introductory statistics course. The students sre asked to come to the laboratory 15 minutes before the final exam. In the lab, the psychologist record physiological measures of anxiety (heart rate, skin resistance, blood pressure, and so on) for each participant. In addition, the psychologist obtains the exam score for each participant.
Student Anxiety Rating Exam Score
A 3 81
B 4 83
C 7 80
D 6 81
E 2 87
F 7 82
G 5 79
a. Compute the Pearson correlation for the data. Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all steps and all parts of all answers. b. Is there a significant relationship between anxiety and exam score? Use a two-tailed test with alpha =.05. Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all steps and all parts of all answers.
Solutions
Expert Solution
The table given below ,
| X | Y | X^2 | Y^2 | XY | |
| 3 | 81 | 9 | 6561 | 243 | |
| 4 | 83 | 16 | 6889 | 332 | |
| 7 | 80 | 49 | 6400 | 560 | |
| 6 | 81 | 36 | 6561 | 486 | |
| 2 | 87 | 4 | 7569 | 174 | |
| 7 | 82 | 49 | 6724 | 574 | |
| 5 | 79 | 25 | 6241 | 395 | |
| Sum | 34 | 573 | 188 | 46945 | 2764 |
From table ,
(a) Therefore , the Pearson's correlation coefficient is ,
(b) Hypothesis : 
Vs 
The test statistic is ,
The critical value is ,
; From excel , "=TINV(0.05,5)"
Rejection Region : 
Decision : Here , the value of the test statistic does not lies in the rejection region.
Therefore , fail to reject the null hypothesis.
Conclusion : Hence , there is not sufficient evidence to support the claim that there is a significant relationship between anxiety and exam score.
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