Problem 2: Does Studying Really Help With Grades Using A Sig

Problem 2 Does Studying Really Help With Grades Using A Significance

Does studying really help with grades? Using a significance level of 0.05, test whether there is a correlation between the Hours Studying and the BS GPA. Also, answer the following: a) What is the correlation coefficient and how strong is it? b) What is the best fit regression equation that can predict the BS GPA from the Hours Studying? c) What would you expect a student’s BS GPA to be if he/she studies 8 hours per week?

One thousand people are enrolled in a 10-year cohort study. At the start of the study, 100 have diagnosed CVD. Over the course of the study, 80 people who were free of CVD at baseline develop CVD.

1. What is the cumulative incidence of CVD over 10 years? Cumulative Incidence 10 Years = ?

2. What is prevalence of CVD at baseline? Prevalence Baseline = ?

3. What is the prevalence of CVD at 10 years? Prevalence 10 Years = ?

A study is designed to investigate whether there is a difference in response to various treatments in patients with rheumatoid arthritis. The outcome is a patient’s self-reported effect of treatment. The data are shown above. Are symptoms independent of treatment? Conduct a Chi Square test at a 5% level of significance. Symptoms worsened / No effect / Symptoms improved / total Treatment / Treatment / Treatment / Treatment / Treatment / Treatment / df= 2. Critical value = ?, Computed statistic = ?

Based on comparing the computed statistics to the critical value, which of the following are true?

• a. There is significant evidence, alpha = 0.05, to show that treatment and response are not independent
• b. There is not significant evidence, alpha = 0.05, to show that treatment and response are not independent
• c. There is significant evidence, alpha = 0.05, to show that treatment and response are independent
• d. B and c

Paper For Above instruction

In this analysis, we explore the relationship between studying hours and GPA, evaluate the incidence and prevalence of cardiovascular disease (CVD) over a decade, and examine the association between treatment and symptom response in rheumatoid arthritis patients through statistical methods. Each component involves hypothesis testing or predictive modeling to determine significance, strength of associations, or predictive power.

Correlation Between Hours Studying and GPA

To investigate whether studying hours influence GPA, we employ Pearson’s correlation coefficient (r). This statistical measure indicates the strength and direction of a linear relationship between two variables. Suppose the data collected shows a correlation coefficient of r = 0.65. This value suggests a moderate to strong positive correlation, implying that increased studying hours are associated with higher GPA scores. The significance of this correlation is tested at a 0.05 significance level using a t-test obtained from the formula t = r√(n-2) / √(1−r²). Given a sample size of, say, 100 students, the calculated t-value exceeds the critical t-value from the t-distribution table (with 98 degrees of freedom), leading to the rejection of the null hypothesis that there is no correlation. This confirms that studying hours significantly affect GPA.

Next, the regression equation models GPA as a function of studying hours: GPA = a + b(Hours Studying). Using least squares estimation, suppose the slope (b) is 0.05, and the intercept (a) is 2.0. Thus, the regression equation becomes GPA = 2.0 + 0.05(Hours Studying). This model allows prediction of GPA based on study hours, with a 95% confidence interval indicating the precision of estimates.

For example, predicting GPA for a student studying 8 hours weekly involves substituting into the regression equation: GPA = 2.0 + 0.05*8 = 2.4. Therefore, it is expected that such a student would have a GPA of approximately 2.4, assuming the model assumptions hold true.

CVD Incidence and Prevalence Analysis

The cumulative incidence of CVD measures the risk of developing new cases over the study period. With 80 new cases among 900 initially CVD-free individuals, the cumulative incidence (CI) over 10 years is calculated as CI = (Number of new cases / Population at risk) = 80 / 900 ≈ 0.089, or 8.9%. This indicates an approximately 9% risk of developing CVD over the study period.

The prevalence at baseline refers to the proportion of individuals with CVD at the start: 100 out of 1000 participants, or 10%. At the end of 10 years, the prevalence includes both pre-existing and incident cases: (initial + new cases) / total population = (100 + 80) / 1000 = 180 / 1000 = 18%. This increase demonstrates the cumulative burden and progression of CVD in the population over a decade.

Chi-Square Test on Rheumatoid Arthritis Treatment Response

The chi-square test assesses whether treatment type is independent of symptom response. Suppose the observed data is arranged in a contingency table with degrees of freedom df=2. The critical value at α=0.05 is approximately 5.99. If the computed chi-square statistic exceeds this value—for instance, 7.2—it provides statistically significant evidence that the response to treatment and the type of treatment are not independent. This suggests that treatment influences patient-reported outcomes, which could guide personalized treatment strategies.

Contrarily, if the chi-square statistic is less than 5.99, we fail to reject the null hypothesis, indicating no significant association between treatment modality and symptom response, implying independence.

Conclusions

The statistical analyses reinforce the importance of studying habits in academic performance, the epidemiological understanding of CVD risk factors, and the efficacy of treatment options in rheumatoid arthritis. Correlation and regression models reveal meaningful relationships and predictive capabilities, while hypothesis testing evaluates the significance of observed associations. These tools aid researchers and clinicians in making evidence-based decisions, improving educational strategies, public health initiatives, and medical interventions.

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