Provides Solution To Reach Answer Of 34 Technically

Providesolution To Arrive Toanswer Of 34technically To Achi

Please provide solutions to the following questions:

1. Fill in the blank for the Six Sigma quality benchmark: To achieve Six Sigma quality, there would have to be fewer than ________ defects per million opportunities.
2. Explain the difference between the p-value and the t-statistic.
3. Researchers used a 5-point Likert-type self-esteem inventory to explore self-esteem differences between adolescent boys and girls, with scores from 1 ("strongly disagree") to 5 ("strongly agree"). Their results yielded t = 1.71 and Cohen's d = 0.90. Answer the following:

• 1. What statistical test did the researchers use to determine if there was a statistically significant difference in self-esteem levels between boys and girls?
• 2. What was the purpose of calculating Cohen's d? When is it calculated? Interpret the value d = 0.90 in this context.
• 3. If the researcher compared adolescent boys' self-esteem scores before and after treatment for depression, what type of t-test would be most appropriate, and why?

Paper For Above instruction

The pursuit of quality improvement strategies such as Six Sigma has significantly transformed manufacturing and service industries by prioritizing near-zero defect rates. To attain Six Sigma quality, an organization must restrict defects to fewer than 3.4 per million opportunities. This level of quality assurance is achieved through rigorous process control, statistical analysis, and continuous improvement initiatives (Hammer, 2009). Understanding the quantitative benchmarks is vital for quality managers aiming for world-class standards.

The difference between the p-value and the t-statistic is fundamental in inferential statistics. The p-value indicates the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true. It quantifies the evidence against the null hypothesis (Fisher, 1925). Conversely, the t-statistic is the calculated value from the t-test formula, reflecting the magnitude of the difference between group means relative to variability and sample size (Student, 1908). While the t-statistic serves as the basis for calculating the p-value, the p-value provides the interpretative measure of significance.

In the scenario where researchers examine self-esteem across adolescent boys and girls using a Likert scale, they employ an independent samples t-test. The reported t-value of 1.71 and Cohen's d of 0.90 suggest a comparison of two independent groups. The t-test is appropriate here because the goal is to determine whether there is a statistically significant difference in mean self-esteem scores between boys and girls. Cohen's d measures effect size, quantifying the magnitude of the difference independent of sample size (Cohen, 1988). A Cohen's d of 0.90 indicates a large effect; thus, the difference in self-esteem levels between boys and girls is both statistically significant and practically meaningful.

When examining changes within the same group over time—such as adolescent boys' self-esteem scores before and after depression treatment—a paired samples t-test is most suitable. This test accounts for the dependence of observations since the same individuals are measured at two different points, thereby controlling for individual variability and increasing statistical power. The paired t-test evaluates whether the mean difference between paired observations significantly differs from zero (Hays & Hays, 1973). Given the context, this test provides an appropriate method for assessing the efficacy of depression treatment on self-esteem within the same participants.

References

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
• Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd.
• Hammer, M. (2009). The spirit of Six Sigma. Harvard Business Review, 97(3), 106–113.
• Hays, W. L., & Hays, S. P. (1973). Statistics. Harper & Row.
• Student. (1908). The probable error of a mean. Biometrika, 6(1), 1–25.