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?
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?
You might want to try a Mann-Whitney U Test as an nonparametric alternative to the Independent Groups T-test since the data tends to be skewed. Nonparametric tests can be used for data that do not follow a normal distribution.
a. The data provided involves comparing two groups (students who do not perform community service vs. students who do), and the goal is to determine if there is a significant difference between their Christian maturity levels. As the Christian maturity scores are skewed, it would be appropriate to use a non-parametric test, specifically the Mann-Whitney U test.
b. The Mann-Whitney U test is a two-tailed test. It tests whether there is a significant difference between the groups, regardless of the direction of the difference.
c. H0 (null hypothesis): There is no significant difference in Christian maturity scores between students who do not perform community service and those who do.
Ha (alternative hypothesis): There is a significant difference in Christian maturity scores between students who do not perform community service and those who do.
d. To conduct the analysis, follow these steps:
1. Calculate the U statistic, which is a measure of the rank sums of the two groups.
2. Convert the U statistic into a Z-score using the appropriate formula.
3. Determine the p-value using the Z-score.
e. To determine whether H0 should be rejected, compare the calculated p-value to the predetermined significance level (typically 0.05). If the p-value is less than the significance level, then H0 can be rejected. The researcher should conclude that there is a significant difference in Christian maturity levels between students who do and do not perform community service. Conversely, if the p-value is greater than the significance level, there is not enough evidence to reject H0, and the researcher cannot conclude that there is a significant difference in Christian maturity levels.