The student must then post 1 reply to another student’s post. The reply must summarize thestudent’s findings and indicate areas of agreement, disagreement, and improvement. It must besupported with scholarly citations in the latest APA format and corresponding list of references.The minimum word count for Integrating Faith and Learning discussion reply is 250 words.
D7.9.1
D7.9.1.a Under What Conditions Would You Use a One-Sample T Test?
A one-sample t test is used when comparing the mean of a single sample to a known or hypothesized population mean, assuming the dependent variable is normally distributed and the data are independent (Morgan et al., 2019).
D7.9.1.b Provide Another Possible Example of Its Use from the HSB Data.
From the HSB data, an example would be comparing the sample mean SAT Math score to the national average of 500. For instance, if the HSB sample mean was 515, a one-sample t test could show whether this difference from 500 is statistically meaningful. This would help decide if students in the sample are scoring higher (or lower) than the national benchmark, rather than the difference being due to chance.
D7.9.2 In Output 9.2
D7.9.2.a Are the Variances Equal or Significantly Different for the Three Dependent Variables?
Levene’s test shows that the assumption of equal variances holds for math achievement (p = .466) and grades in high school (p = .451), but not for visualization (p = .013). For visualization, the equal variances not assumed row must be used.
D7.9.2.b List the Appropriate t, df, and p (Significance Level) for Each t test As You Would in an Article.
The independent-samples t test showed that fast track students scored significantly higher on math achievement, t(73) = 2.70, p = .009. For grades in high school, there was no significant difference between groups, t(73) = -0.90, p = .369. For visualization, the test also showed a significant difference, t(57.15) = 2.39, p = .020.
D7.9.2.c Which t tests Are Statistically Significant?
Math achievement and visualization showed statistically significant differences between fast track and regular track students, meaning students in the fast track performed better in these areas. In contrast, grades in high school were not statistically significant, showing that both groups earned similar overall grades despite differences in test performance.
D7.9.2.d Write Sentences Interpreting the Academic Track Difference Between the Means of Grades in High School and Also Visualization.
Students in the fast track scored significantly higher on math achievement and visualization compared to regular track students. For grades in high school, there was no meaningful difference.
D7.9.2.e Interpret the 95% Confidence Interval for These Two Variables.
For math achievement, the 95% CI (1.05 to 6.97) indicates the true difference in means is likely between about one and seven points, confirming significance. For grades, the CI includes zero (-1.06 to .40), showing no real difference. For visualization, the CI (.35 to 3.98) shows fast track students scored higher, and the interval does not include zero.
D7.9.2.f Comment on the Effect Sizes.
Effect sizes (Cohen’s d) suggest that the difference in math achievement is medium-to-large (about .60), the difference in visualization is small-to-medium, and the difference in grades is trivial.
D7.9.3
D7.9.3.a Compare the Results of Outputs 9.2 and 9.3.
The results from Output 9.2 (t tests) and Output 9.3 (Mann–Whitney U tests) tell the same overall story. Both tests found significant differences between fast track and regular track students on math achievement (U = 455.5, p = .010) and visualization (U = 505.0, p = .040). In both cases, fast track students scored higher, as shown by their higher mean ranks (45.10 vs. 32.11 for math; 43.65 vs. 33.32 for visualization). For grades in high school, the Mann–Whitney U test confirmed no significant difference (U = 621.5, p = .413), consistent with the independent-samples t test.
D7.9.3.b When Would You Use the Mann–Whitney U Test?
The Mann–Whitney U test is used when the assumptions of the independent-samples t test (such as normal distribution) may be violated, or when the data are ordinal rather than interval/ratio. It is a nonparametric alternative that compares the ranks of scores between groups instead of comparing means.
D7.9.4 In Output 9.4
D7.9.4.a What Does the Paired Samples Correlation for Mother’s and Father’s Education Mean?
The paired samples correlation (r = .68, p < .001) shows that mother’s and father’s education levels are strongly related. In other words, when one parent has more education, the other parent tends to as well.
D7.9.4.b Interpret/Explain the Results for the T Test.
The paired t test compares the average education levels directly. Fathers had a higher mean education level (M = 4.73) than mothers (M = 4.14). This difference of about .59 years of education was statistically significant, t(72) = 2.40, p = .019.
D7.9.4.c Explain How the Correlation and the T Test Differ in What Information They Provide.
The correlation and t test provide different information. The correlation shows how strongly the two variables move together, while the t test shows whether there is a meaningful difference in the average level of education between mothers and fathers.
D7.9.4.d Describe the Results if the r Was .90 and the t Was Zero.
If r = .90 and t = 0, it would mean that mothers’ and fathers’ education levels are almost perfectly related (very strong correlation), but their averages are the same with no significant difference.
D7.9.4.e What if r Was Zero and t Was 5.0?
If r = 0 and t = 5.0, it would mean that there is no relationship between mothers’ and fathers’ education levels, but the average education is very different between the two groups.
D7.9.5
D7.9.5.a Compare the Results of Output 9.4 with Output 9.5.
The results from Output 9.4 (paired t test) and Output 9.5 (Wilcoxon Signed Ranks test) lead to the same conclusion about parents’ education. Both tests show that fathers had significantly higher education levels than mothers. The paired t test gave t(72) = 2.40, p = .019, while the Wilcoxon test also found a significant difference, Z = –2.09, p = .037. For visualization vs. visualization 2, the Wilcoxon test showed no significant difference (p = .709), which confirms that scores did not change meaningfully between the two visualization measures.
D7.9.5.b When Would You Use the Wilcoxon Test?
The Wilcoxon test is a nonparametric alternative to the paired t test. It is used when the assumptions of the paired t test are not met (such as normality of the difference scores) or when the data are ordinal. Instead of comparing means, it compares the ranks of differences to see if one condition is consistently higher than the other.
References
Morgan, G. A., Leech, N. L., Gloeckner, G. W., & Barrett, K. C. (2019). IBM SPSS for introductory statistics: Use and interpretation (6th ed.). Routledge.
