Stat 305 Fall 2020 SFU Midterm Due October 23 500 Pm PST ✓ Solved

Stat305605 Fall 2020 Sfu Midterm Due October 23rd 500pm Pstmidterm E

The assignment involves completing the first problem and one of the remaining two problems from a midterm exam. The exam covers multiple-choice questions regarding the appropriate statistical test for given scenarios, Bayesian probability calculations for HIV testing, and t-test applications related to sports participation data. The exam is open book, and answers must be uploaded via Crowdmark. A response to the honor code must also be submitted.

Specifically, students must analyze multiple scenarios: selecting appropriate statistical tests for associations between health variables, response to treatments, trends over time, and other data-driven hypotheses. The second problem involves applying Bayes’ rule to assess probabilities related to HIV testing sensitivity, specificity, and prevalence data. The third problem focuses on conducting and interpreting a two-sample t-test with real data on sports participation, including critical evaluation of the statistical conclusion and validity of interpretations.

Students are required to show work for calculations, upload responses in PDF format, and adhere to the provided instructions for a comprehensive assessment of their statistical understanding and reasoning. The task emphasizes critical thinking, statistical application, and ethical academic conduct throughout.

Sample Paper For Above instruction

Introduction

This essay addresses the core components of the midterm exam in STAT305/605 for Fall 2020, focusing on critical statistical decision-making, Bayesian analysis, and hypothesis testing. The questions are designed to evaluate understanding of selection of appropriate statistical tests, probabilistic reasoning in medical diagnostics, and data interpretation within real-world contexts, particularly health sciences and sports studies.

Question 1: Selecting Appropriate Statistical Tests

The first problem presents scenarios where identifying the most suitable statistical test is essential. For the association between blood pressure and cortisol levels, the correlation test with the null hypothesis that their Pearson correlation coefficient is zero is appropriate, because it directly measures the strength and direction of the linear relationship between two continuous variables (Schober et al., 2018). This test can determine if there is evidence to suggest an association without implying causation.

In the second scenario involving the effect of a treatment on COVID-19 duration, a one-sided two-sample unpaired t-test comparing treatment and control group means, with the null hypothesis that the mean duration under treatment is not less than that without treatment, is suitable. This test assesses whether the treatment reduces the duration, respecting the hypothesis's directional nature (Cohen, 1988).

The third scenario involves assessing whether measures to reduce ambulance accidents have led to improvements over the last decade. The most relevant statistical quantity is the linear regression coefficient between the accident ratio and year t. This metric quantifies the trend over time, with a significant negative coefficient indicating improvement (Kutner et al., 2004).

Question 2: Bayesian Probability in HIV Testing

The second problem involves applying Bayes’ rule to evaluate the probability that a child is uninfected given a positive test, considering test sensitivity, specificity, and prevalence. The calculations involve the prior probability of infection, the likelihood of positive tests given true infection status, and the overall probability of testing positive, which together determine the posterior probability that the child does not have HIV (Gelman et al., 2013).

When the test's sensitivity is 100%, and the specificity is 99.4%, the probability that a positive test truly indicates infection is high, but false positives remain possible due to imperfect specificity. The Bayesian formula yields a relatively low probability that a child is uninfected after a positive result, emphasizing the importance of confirmatory testing.

In scenarios involving population prevalence and repeated testing, the updated probabilities reflect the interplay between prior prevalence and test accuracy, underscoring Bayesian inference's utility in medical diagnostics (Rothman et al., 2008).

Question 3: T-Tests in Sports Participation Research

The third problem involves conducting a two-sample t-test with given data comparing participation in months between classes with different curricula. Calculating the sample means, variances, and degrees of freedom enables computing the p-value to test the null hypothesis that there is no difference in mean participation (Welch, 1938).

If the p-value is below the significance level (0.05), it indicates statistically significant evidence that the new curriculum influences participation. Critical interpretation involves considering the effect size, potential biases, and the assumptions underlying the t-test, such as normality and variance heterogeneity.

Furthermore, critique and contextual analysis should consider sample sizes, data distribution, and external factors affecting participation, emphasizing the importance of statistical literacy in educational research.

Conclusion

The midterm exam challenges students to apply foundational and advanced statistical concepts to real-world scenarios, fostering analytical competence and ethical responsibility. Carefully selecting appropriate methods, understanding probability models, and critically evaluating results are crucial skills for data-informed decision-making in health, research, and policy.

References

• Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences. Routledge.
• Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis. CRC press.
• Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2004). Applied Linear Statistical Models. McGraw-Hill/Irwin.
• Schober, P., Boer, C., & Schwarte, L. A. (2018). Correlation Coefficients: Appropriate Use and Interpretation. Anesthesia & Analgesia, 126(5), 1763–1768.
• Rosenbaum, P. R. (2002). Observational Studies. Springer.
• Welch, B. L. (1938). The Significance Test for Variance Heterogeneity. Biometrika, 29(3-4), 350–362.
• Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern Epidemiology. Lippincott Williams & Wilkins.
• Shapiro, S. S., & Wilk, M. B. (1965). An Analysis of Variance Test for Normality. Biometrika, 52(3-4), 591–611.
• Statistical Office of Canada. (2010). Participation in Sports and Physical Activities among Canadian Youths. Statistics Canada.

In summary, this essay synthesizes the key components of the midterm exam, highlighting the importance of method selection, probability reasoning, and critical interpretation in applied statistics. These skills are essential for advancing knowledge in health sciences, education, and policy analysis.