In a regression analysis, a nurse researcher found a correlation of .82 between pain relief scores and satisfaction with nursing care. She also calculated the following for her regression analysis:
Pain Relief (x): Mean = 58 sd = 3.9
Satisfaction (y): Mean = 42 sd = 4.4
slope = 1.56
y intercept = - 3.53
Q1. What will be the predicted satisfaction score (expressed as a point estimate) for a patient with a pain relief score of 62?
Y = bX + a
Y=1.56(62)+-3.53
=93.19
Q2. What is the standard error of estimate when predicting satisfaction from knowledge of pain relief score?
Sy.x =sdY √ 1 - r2
=4.4+ 1-.82^2==.3276 or .33
Q3. What would be the interval estimate for satisfaction for the patient in problem 16?
Items 19-21: A nurse researcher is investigating the effect of timing of standard pain control interventions on severity of pain in adolescents with sickle-cell disease. She establishes three treatment protocols: 1) initiation of pain control immediately upon the presence of prodromal sign (an "aura" signaling the imminent onset of pain); 2) initiation of pain control one hour after the onset of pain; and 3) initiation of pain control only at the points where non-steroidal anti-inflammatories and guided imagery are no longer effective in keeping pain bearable. She conducted a one-way ANOVA to analyze her data and the following table summarizes her findings:
Source df SS MSS F p
Among 2 75536.2 37768.1 5.159 <.05
Within 27 197660.3 7320.8
Total 29 273196.5
On the basis of these data alone, she drew the following conclusions. For each conclusion, indicate whether you feel the conclusion is justified or unjustified.
Q4. Severity of pain is influenced by the timing of pain interventions in sickle-cell crises.
Q5 Immediate intervention is better than either slightly delayed intervention or initiation at crisis stage.
Q6. She has more than 99% confidence in her conclusion that severity of pain is influenced by timing.
Items 22-23 relate to the following study results:
Study A Study B
r = .64 r = .77
df = 18 df = 121
p<.05 p<.01
Q7. In using the data from study A to make predictions, what percent of the time would you expect predictions to be exactly correct?
Q8. Which study would have the smallest margin of error in predicting one variable from knowledge of the other?
Items 24 and 25 relate to the following SPSS output. A researcher is interested in characteristics of HIV+ and HIV- adolescents interviewed 166 young adults about their experiences during adolescence. He wished to know, among other things, if there were significant differences in the ages at which HIV+ and HIV- young adults became sexually active. The following is the printout of this analysis:
HIV Status N Mean sd Stnd. Error
Age at Positive 57 13.2 2.96576 .39282
first sexual
experience Negative 109 15.1 2.57286 .24644
Independent Samples Test
Levene's Test for
Equality of Variances
F Sig
Age at Equal variance assumed 1.313 .254
first sexual
experience Equal variance not assumed
t-test for Equality of Means
t df sig. mean difference
Age at Equal variance assumed -2.870 164 .005 -1.9
first sexual
experience Equal variance not assumed -2.745 99.66 .007 -1.9
Q9. Were there significant differences between the groups. Give the relevant stastical data to support your answer?
Q10. What is the confidence interval associated with your answer to item # 24?
Each of the questions on the following pages is a calculation problem worth 10 points. Partial credit will be awarded if I can following your procedures and determine that errors are arithmetic rather than conceptual. It would be wise, therefore, to clearly indicate your worksteps on each problem.
Q11. For the following data set, calculate the oneway ANOVA and test for significance at the .05 level.
Group 1 Group 2 Group 3 Group 4
x x2 x x2 x x2 x x2
7 49 10 100 12 144 16 256
8 64 12 144 14 196 15 225
7 49 13 169 13 169 18 324
9 81 13 169 11 121 17 289
9 81 14 196 13 169 20 400
11 121 15 225 15 225 21 441
10 100 14 196 13 169 22 484
61 545 91 1,199 91 1,193 129 2,419
Q12. Evaluate the χ2 for the following 3 X 2 table and test for significance at the .01 level.
Group 1 Group 2 Group 3
Positive
Outcome 9 12 8 29
Negative
Outcome 5 16 4 25
14 28 12 54
Q13. For the subsequent paired observations, determine the Pearson product-moment correlation coefficient and test for significance at the .01 level.
x x2 y y2 xy
17 289 23 529 391
17 289 19 361 323
18 324 20 400 360
19 361 17 289 323
21 441 15 225 315
22 484 19 361 418
21 441 20 400 420
23 529 19 361 437
22 484 20 400 440
18 324 16 256 288
198 3,966 188 3,582 3,715
Q14. For the following paired observations, calculate the Pearson product-moment correlation coefficient and test for significance at the .01 level.
x x2 y y2 xy
17 289 23 529 391
17 289 19 361 323
18 324 20 400 360
19 361 17 289 323
21 441 15 225 315
22 484 19 361 418
21 441 20 400 420
23 529 19 361 437
22 484 20 400 440
18 324 16 256 288
198 3,966 188 3,582 3,715
Q15. For the following data regarding paired rank orders for a sample, calculate the correlation coefficient and test for significance at the .05 level.
Subject # Rank 1 Rank 2
1 2 1
2 1 2.5
3 3 2.5
4 5 4
5 6 5
6 4 8
7 7 6
8 9 7
9 8 10
10 10 9