3. A researcher is interested in comparing the Christian maturity level of students who volunteer for community service versus those who do not. The researcher assumes that those who perform community service will have higher Christian maturity scores. The maturity scores tend to be skewed (not normally distributed). Higher scores indicate higher Christian maturity.

No Community Service Community Service
32 47
40 48
54 59
13 72
20 80
26 55

a. What statistical test should be used to analyze these data?
Wilcoxon Rank Sum test

b. Is this a one- or two- tailed test?

c. Identify H0 and Ha for this study
d. Conduct the appropriate analysis
e. Should H0 be rejected? What should the researcher conclude?

b. This is a one-tailed test.

c. H0 (Null hypothesis): There is no difference in Christian maturity levels between students who volunteer for community service and those who do not.
Ha (Alternative hypothesis): Students who volunteer for community service have higher Christian maturity levels compared to those who do not.

d. To conduct the appropriate analysis, we can use the Wilcoxon Rank Sum test (also known as the Mann-Whitney U test) because the data is not normally distributed.

e. After conducting the test, we need to compare the p-value obtained with the significance level (e.g., α = 0.05). If the p-value is less than the significance level, then H0 should be rejected, indicating that there is a significant difference in Christian maturity levels between students who volunteer for community service and those who do not. On the other hand, if the p-value is greater than the significance level, then H0 should not be rejected, suggesting that there is no significant difference in Christian maturity levels between the two groups. The researcher should conclude based on the results of the statistical test.