Deliverable 05 – Worksheet Instructions: The Following Works

Deliverable 05 – Worksheet Instructions: The following worksheet describes two examples

The assignment involves analyzing two statistical scenarios: one concerning independent samples and the other related to dependent samples. The goal is to demonstrate detailed solutions for each example, explaining all steps thoroughly in your own words. For the independent samples scenario, you will test whether a new drug reduces systolic blood pressure using a significance level of 0.01 and the critical value method, given unknown population standard deviations. For the dependent samples scenario, you will analyze if the drug lowers blood pressure within the same group, using a significance level of 0.05 and the p-value method.

Paper For Above instruction

The evaluation of a new antihypertensive drug's effectiveness involves two key statistical analyses: an independent samples t-test and a dependent samples t-test. These tests help determine whether the observed changes in blood pressure are statistically significant, supporting or refuting the drug's efficacy.

Analysis of Independent Samples

The scenario involves comparing the mean systolic blood pressure between two unrelated groups: one receiving the drug (treatment group) and a control group not receiving the drug. The hypotheses are formulated as follows:

  • Null hypothesis (H₀):μ₁ ≥ μ₂, meaning the drug does not reduce blood pressure.
  • Alternative hypothesis (H₁):μ₁

This is a left-tailed test because the claim specifies a reduction (less than). We choose a significance level (α) of 0.01 to control the probability of Type I error, ensuring high confidence in the results.

To test this, we first compute the test statistic using the formula for two independent samples with unequal variances (Welch’s t-test):

t = (bar_x₁ - bar_x₂) / √(s₁²/n₁ + s₂²/n₂)

Where

- bar_x₁ and bar_x₂ represent sample means,

- s₁ and s₂ are sample standard deviations,

- n₁ and n₂ are sample sizes.

Calculating the degrees of freedom (df) involves the Welch-Satterthwaite equation. Once the test statistic t and df are computed, the critical value (t_critical) for α = 0.01 and df from t-distribution tables or software is identified. If t

Analysis of Dependent Samples

The second part involves measuring blood pressure before and after administering the drug to the same group, creating paired data. The hypotheses are:

  • Null hypothesis (H₀):μ_d ≤ 0, where μ_d is the mean difference in blood pressure.
  • Alternative hypothesis (H₁):μ_d > 0, suggesting the drug lowers blood pressure (difference greater than zero). This is a right-tailed test.

The significance level is set at 0.05. The analysis involves calculating the mean difference and its standard deviation, then computing the test statistic for paired samples:

t = (mean difference) / (standard deviation of differences / √n)

Using the calculated t, the p-value is obtained from the t-distribution. If the p-value is less than 0.05, we reject H₀, supporting the claim that the drug helps lower blood pressure.

In conclusion, these analyses allow us to assess the efficacy of the new drug using rigorous statistical methods, providing evidence either in favor or against its effectiveness.

References

  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage.
  • McDonald, J. H. (2014). Handbook of Biological Statistics. Sparky House Publishing.
  • Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
  • Chapman, S. (2015). Statistics in Psychology and Education. Pearson.
  • Gibbons, J. D., & Chakraborti, S. (2011). Nonparametric Statistical Inference. CRC Press.
  • Bluman, A. G. (2012). Elementary Statistics: A Step By Step Approach. McGraw-Hill Education.
  • Russell, K. C. (2020). Introduction to Biostatistics. John Wiley & Sons.
  • Zimmerman, D. W. (2006). A note on the use of the t-test for related samples. Journal of Educational and Behavioral Statistics, 31(2), 250-260.
  • Noreen, E. (2018). Corporate Data Analysis. Routledge.
  • Agresti, A. (2018). Statistical Thinking: Improving Business Decision Making. CRC Press.

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