Deliverable 05 Worksheet Instructions: The Following ✓ Solved

Deliverable 05 Worksheet Instructions: The following

Deliverable 05 – Worksheet Instructions: The following worksheet describes two examples – one is an example for independent samples and the other one for dependent samples. Your job is to demonstrate the solution to each scenario by showing how to work through each example in detail. You are expected to explain all of the steps in your own words.

1) Independent samples: One of our researchers wishes to determine whether people with high blood pressure can reduce their systolic blood pressure by taking a new drug we have developed. The sample data is shown below, where xÌ…1 represents the mean blood pressure of the treatment group and xÌ…2 represents the mean for the control group. Use a significance level of 0.05 and the critical value method to test the claim that the diet reduces the blood pressure. We do not know the values of the population standard deviations. Please use the following critical value for this test: 2.378. Treatment Group Control Group n n..7 s.7 s.2 Answer and Explanation Enter your step-by-step description and explanations here.

2) Dependent samples This same new drug was tested on another group, but this time the test was done before the drug was administered, and then tested after the drug was given to the same group. The results are shown in the table below: Subject Before After Answer and Explanation Enter your step-by-step description and explanations here. t =±

Paper For Above Instructions

In order to tackle the analyses of the independent and dependent samples from the provided examples comprehensively, we will follow a systematic approach to apply the statistical methods relevant to each case. Let’s begin with the first scenario: the independent samples test involving individuals with high blood pressure.

Independent Samples Analysis

The goal of the independent samples test is to determine whether the new drug has a significant effect on reducing systolic blood pressure. We will use a significance level (α) of 0.05.

First, we need to establish our null hypothesis (H₀) and alternative hypothesis (H_a):

• H₀: There is no difference in mean blood pressure between the treatment group and the control group (μ₁ - μ₂ = 0).
• H_a: The treatment group has a lower mean blood pressure than the control group (μ₁ - μ₂

Next, let’s denote important parameters:

• n₁ = sample size of treatment group,
• n₂ = sample size of control group,
• s₁ = standard deviation of treatment group,
• s₂ = standard deviation of control group,
• x̄₁ = mean blood pressure of treatment group,
• x̄₂ = mean blood pressure of control group.

Given that we do not know the population standard deviations, we will apply the t-test for independent samples, which can be computed using the formula:

t = (x̄₁ - x̄₂) / √((s₁²/n₁) + (s₂²/n₂))

With the critical value for the t-test being 2.378, we compare our calculated t with this critical value.

If the computed t is less than -2.378, we will reject the null hypothesis, concluding that the drug effectively lowers blood pressure.

Dependent Samples Analysis

In the dependent samples scenario, the same subjects are tested before and after administering the drug. The aim here is to analyze whether there is a significant difference in the systolic blood pressure before and after treatment.

We set our hypotheses as follows:

• H₀: There is no difference in mean systolic blood pressure before and after treatment (μ_before - μ_after = 0).
• H_a: There is a reduction in mean systolic blood pressure after treatment (μ_before - μ_after > 0).

To perform the analysis, we compute the differences in blood pressure readings before and after treatment:

• d_i = Blood pressure before treatment - Blood pressure after treatment

We then calculate the mean difference (d̄) and standard deviation of the differences (s_d).

The t-statistic for a dependent samples test is computed as follows:

t = d̄ / (s_d/√n)

Where n is the number of paired observations. Once again, we compare the computed t-value to the critical value, and if it exceeds the designated threshold (typically 1.833 for a paired t-test depending on degrees of freedom), we reject the null hypothesis.

Conclusion

Through the analyses of both independent and dependent samples above, we have demonstrated the steps involved in applying t-tests to ascertain whether the new drug effectively reduces blood pressure. By careful hypothesis formulation, calculation of t-statistics, and consideration of critical values, conclusions can be drawn regarding the efficacy of the treatment.

References

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• Sullivan, L. M., & Massaro, J. M. (2011). Essentials of Biostatistics in Public Health. Jones & Bartlett Learning.
• Granowo, A., & Wu, R. (2020). Statistical considerations in the interpretation of clinical studies. Clinical Research, 35(4).
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