Proportions (Essay Sample)
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
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
Norman, G., and Streiner, D. (2008). Comparing Two Groups: the t-Test. Biostatistics The Bare Essentials. 3rd Edition. BC Decker Inc. PMPH USA, Ltd. Shelton, CT. eISBN: 9781607950585 pISBN: 9781550093476. Available in Ebrary, accessed via Trident’s online library.
Norman, G., and Streiner, D. (2008). Chapter the Twenty First: Tests of Significance for Categorical Frequency Data (pages 235-241). In: Biostatistics The Bare Essentials. 3rd Edition. BC Decker Inc. PMPH USA, Ltd. Shelton, CT. eISBN: 9781607950585 pISBN: 9781550093476. Available in Ebrary, accessed via Trident’s online library.
Peat, J. and Barton, B. (2008). Chapter 6: Continuous Data Analyses: Correlation and Regression. Medical Statistics and Critical Appraisal. Wiley. Chichester, England. Available in Ebrary, accessed via Trident’s online library. *Please note that you only need to read the first section on correlation; the section on regression is an advanced topic beyond the scope of this course.
Briefly describe the procedure for testing hypotheses
Hypothesis testing focuses on assessing the validity of evidence depending on the null and alternative hypothesis. To know which of the hypotheses is true, there is a need to make decision based on the evidence available. It is necessary to first specify the null and alternative hypothesis, with the null hypothesis assumed to be the parameter that is equal to zero. The next step is to specify the level of significance (Î±), mainly 0.01 and 0.05. The next phase in testing hypotheses is the computation of the probability value (P-value), which determines whether the sample statistic has the same characteristic as the parameter specified when the null hypothesis is true. Then one compares the p- value with significance level, which shows whether to reject or not reject the null hypothesis. At other times, it is necessary mapping the area under the curve as this shows the critical value and comparing, with the p-value to determine whether it is statistically significant. The main goal in hypothesis testing is establish if the evidence available can help to infer whether the null hypothesis is unlikely to be true, with the alternative hypothesis then being true (Norman & Streiner, 2008).
Formulate the null and alternative hypotheses
H0: Cholesterol treatment is not effective
H1: Cholesterol treatment is effective
The null hypothesis assumes that even after intervention there are no noticeable changes, while the alternative hypothesis states that treatment/ intervention results in changes (Norman & Streiner, 2008). In this case, the expected change as ...
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