Deliverable 05 Worksheet Instructions: The Following 477176

Deliverable 05 Worksheet instructions: the Following Worksheet Describ

The worksheet requires presenting detailed solutions for two statistical scenarios: one involving independent samples and the other dependent samples. For each scenario, you are to clearly articulate all analytical steps in your own words, including formulating hypotheses, calculating critical values and test statistics, and making data-driven decisions regarding the null hypothesis. Use a significance level of 0.01 for the independent samples test and 0.05 for the dependent samples test. For the independent samples case, determine whether the test is right-tailed, left-tailed, or two-tailed, and explain the rationale. For the dependent samples, employ the P-value method to evaluate whether the population mean difference exceeds zero, based on the provided data. Discuss your conclusions in non-technical terms, summarizing whether there is sufficient evidence to support the claims made about the drug's effect on blood pressure.

Paper For Above instruction

The analysis of clinical interventions often requires rigorous statistical testing to evaluate the effectiveness of treatments. This paper explores two fundamental statistical approaches—independent samples t-test and dependent samples t-test—in the context of assessing a new antihypertensive drug's efficacy on lowering systolic blood pressure.

Independent Samples T-Test: Evaluating Blood Pressure Reduction

The first scenario involves an independent samples t-test designed to determine whether the new drug significantly reduces systolic blood pressure in patients with hypertension compared to a control group. The sample data provided indicates the mean blood pressures and standard deviations for both groups, with sample sizes of 80 and 70, respectively. The null hypothesis (H₀) posits no difference between the treatment and control group means, formulated as H₀: μ₁ = μ₂. The alternative hypothesis (H₁) contends that the treatment group mean is less than the control group mean, reflecting a one-tailed test: H₁: μ₁

Calculating the critical value involves using the t-distribution with degrees of freedom (df) calculated as n₁ + n₂ - 2, which totals 148 in this case. Employing the Excel function =TINV(0.01, 148), the critical t-value is approximately -2.60. The test statistic is computed based on sample means, standard deviations, and sizes, resulting in a t-value of approximately -2.0. Comparing this t-statistic to the critical value demonstrates that the calculated t is within the acceptance region, indicating insufficient evidence to reject the null hypothesis. Consequently, we conclude that at the 1% significance level, there is not enough statistical evidence to assert that the drug reduces systolic blood pressure relative to the control.

Dependent Samples T-Test: Assessing Blood Pressure Changes Before and After Treatment

The second scenario investigates the same group of patients before and after receiving the drug, utilizing a dependent (paired samples) t-test. The data comprises blood pressure measurements for 12 subjects, with mean differences and standard deviations calculated from individual paired observations. The hypotheses are set as H₀: μ_d = 0, indicating no change, versus H₁: μ_d > 0, supporting the claim that the drug lowers blood pressure, making this a right-tailed test.

The degrees of freedom for the paired t-test is n - 1, which equals 11. Using Excel's =TINV(0.05, 11), the critical t-value is approximately 2.20. The calculated t-statistic, derived from the mean difference of 18 mm Hg and the standard deviation of 10 mm Hg, is approximately 2.72. Since the t-value exceeds the critical value, and the p-value calculated from the t-distribution (using =TDIST(2.72, 11, 1)) is less than 0.05, there is statistically significant evidence to reject the null hypothesis. This indicates that the drug effectively reduces blood pressure in the treated population at the 5% significance level.

Conclusion

The independent samples analysis reveals insufficient evidence at the 1% level to affirm that the drug reduces systolic blood pressure across populations, suggesting the need for further investigation or larger studies. In contrast, the dependent sample analysis provides strong evidence at the 5% level that the drug lowers blood pressure within individuals post-treatment. These findings underscore the importance of choosing appropriate study designs and significance levels tailored to research questions.

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