Population Means And Proportions

Population Means And Proportions

Briefly describe the procedure for testing hypotheses.

The initial step in hypothesis testing involves formulating the null and alternative hypotheses. This can be either one-tailed or two-tailed (Statistics Solutions, n. d). The second step will involve setting the critical value, which determines the acceptance and rejection region. The test statistic is then computed, and the p-value (probability value) and the confidence interval are decided. In this case, the p-value will be set at .05. The fourth step involves decision-making on whether to reject or accept the null hypothesis guided by the test statistic used and the p-value (McBurney & White, 2013). If the p-value is less than .05, we reject the null hypothesis and conclude that the alternative hypothesis is true. Finally, we draw inferences about the data and interpret the results.

Formulate the null and alternative hypotheses.

Precisely, hypothesis testing involves carefully composing two-sided statements: the null hypothesis and alternative hypothesis. In this context, these two should be in line with the study topic about testing the treatment’s effectiveness in controlling cholesterol levels. Therefore, hypotheses can be formulated as follows;

Null Hypothesis (H₀): The treatment is not effective in controlling cholesterol.

Alternative Hypothesis (H₁): The treatment is effective in controlling cholesterol levels

Determine the test statistic that you will use.

Logistic regression in R can be used to test the effectiveness of the treatment in controlling cholesterol. The test statistic is appropriate since it explains the relationship between the treatment and cholesterol control (Washington Edu, 2004). Further, the test is suitable since the variables are not strongly correlated.

Calculate the p-value. Show your work.

Assuming that the trials are normally distributed, we can conduct a logistic regression using R software to determine whether there is enough evidence to conclude that the treatment effectively controls cholesterol and obtains the p-value.

Discuss whether there is enough evidence to reject the null hypothesis.

From the results yielded from the analysis above, the p-value is obtained as 0.081. The p-value is greater than 0.05, and this implies that we fail to reject the null hypothesis. Consequently, this leads to the conclusion that the treatment is not effective in controlling cholesterol.

References

McBurney, D., & White, T. (2013). Research methods. Belmont, CA: Wadsworth Cengage Learning.

Statistics Solutions. (n. d). “Hypothesis Testing” Retrieved from: https://www.statisticssolutions.com/hypothesis-testing2/#:~:text=The%20common%20steps%20in%20all,to%20compute%20the%20test%20statistic.

WashingtonEdu. Courses. (2004). Estimation and hypothesis testing for logistic regression. Retrieved from: https://courses.washington.edu/b515/l13.pdf

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Module 4 – Case: DRAWING INFERENCES ABOUT POPULATION MEANS AND PROPORTIONS

Case Assignment

A researcher conducts a test on the effectiveness of a cholesterol treatment on 114 total subjects. Assuming the tails of distributions are normal distribution, is there evidence that the treatment is effective?

	Cholesterol Decreased	No Cholesterol Decrease	Total
Treatment	38	18	56
No treatment	30	28	58
Total	68	46	114

Submit a (2-3 pages) paper before the end of the module that:

1. Briefly describe the procedure for testing hypotheses.
2. Formulate the null and alternative hypotheses.
3. Determine the test statistic that you will use.
4. Calculate the p-value. Show your work.
5. Discuss whether there is enough evidence to reject the null hypothesis.