ST3003 Assessment
The Normal Distribution and Confidence Intervals
Part 1 — Confidence Intervals in Research
For this section, refer to the following article from the Walden Library:
References
Siamisang, K., Kebadiretse, D., Tjirare, L. T., Muyela, C., Gare, K., & Masupe, T. (2022). Prevalence and predictors of depression, anxiety and stress among frontline healthcare workers at COVID-19 isolation sites in Gaborone, Botswana. PLoS ONE, 17(8), e0273052. https://doi.org/10.1371/journal.pone.0273052
All articles are available in full text in the Walden Library, which you may search by title or DOI. Be sure to provide an explanation for each of your answers and include supporting evidence from the text and/or Learning Resources.
Write responses to address the following in paragraph form by inserting your answers directly beneath the questions.
Table 3 of the journal article displays the number of health care workers who report various levels of depression, anxiety, and stress. These numbers are presented as the number of workers as well as the percent of the total (447). Confidence intervals are given for each percentage value. Choose ONE level of either depression, anxiety, or stress (e.g., normal depression) to use to address the following questions:
ST3003 Assessment
Show how the given percentage was derived based on the sample data.
1. Write 1–2 sentences explaining how the confidence interval would be interpreted.
2. Based on this interval, provide one value that could be considered reasonable as the population proportion and one that would not be considered reasonable as the true population proportion. Fully explain your reasoning.
3. If a subsequent study was completed that increased the sample size to 1,000 participants, explain one change you would expect to see in the confidence intervals. Explain why you feel this change would occur.
Table 1 of this journal article provides a breakdown of characteristics of the 447 participants in this study. The number of participants is given, followed by the percentage in ().
1. Provide one reason you believe a confidence interval was not presented for this data.
Part 2 — Using the Normal Distribution
The following should be based on the data set you created from the larger BODY DATA (ST3001) data set complete the following table:
Smokers Nonsmokers
Mean
Standard deviation
Sample size (n)
Replace the questions below with your response to the following:
Use the table above to answer the following questions based on your individual data. For each question, write a 1-sentence explanation about how Excel was used to assist you in your computations.
Find the percent of smokers expected to have a BMI of greater than 25 (overweight).
1. Find the percent of nonsmokers expected to have a BMI of less than 18.5 (underweight).
2. A normal BMI range is between 18.5 and 24.9. What percent of smokers are expected to be within this range? What percent of nonsmokers are expected to be within this range?
3. A researcher is interested in which BMI represents the 90th percentile (90% are at this BMI level or lower). What BMI score represents the 90th percentile cut-off rate?
ST3003 Assessment
Part 3 — Creating Confidence Intervals
Use the table above when addressing the following.
Complete the following table:
Group 90% confidence interval 95% confidence interval 99% confidence interval
Smokers
Nonsmokers
Replace the questions below with your response to the following:
1. As the level of confidence increases, what happens to the width of the confidence interval? Does it increase or decrease? Explain one reason why this would happen.
Using the 95% confidence interval compare the BMI of smokers vs. nonsmokers. Write a 2–3 sentence paragraph explaining whether these intervals overlap or not. What does that indicate about the differences in BMI between the two groups?
2. In 1–2 sentences, explain the following: What is one situation in which you as a researcher might choose a 99% confidence interval? A 90% interval? Fully justify your choices. Use
APA referencing style.