Week 7 - Lab Assignment

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Chamberlain University College of Nursing *

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MATH225N

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Statistics

Date

Jan 9, 2024

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docx

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Week 7 Lab Assignment Name:______ Instructor Name: ______ 1. Write a paragraph summarizing what you learned from the articles provided. Consider the use of confidence intervals in health sciences with these articles as inspiration and insights. These two articles describe using confidence intervals (CIs) in health sciences research. The first article explains that CIs are a reliable indicator of the soundness of researchers' assumptions about a study population. It explains that a 95% CI, which is the most common level used, means that if researchers were to sample numerous times from the same population and calculate a range of estimates for these samples, 95% of the intervals within the lower and upper limits of this range will include the population value. The second article explains how to compare the CIs of two mean scores to determine whether they are statistically different. It emphasizes that the overlap of the CIs suggests that the scores may represent the same "true" population value. These articles highlight the importance of using CIs in health sciences research to draw sound conclusions about a study population. Data Collection Use the data set you collected for the Week 5 lab (heights of 10 different people plus the 10 heights provided by your instructor). ( NOTE: This is NOT the data used in the lab video, which is about midterm grades. Do not use the midterm grades data.) Provide a screenshot of your Week 5 Data (20 Heights) 1

Summarize the Preliminary Calculations (Round to 2 decimal places): Sample Mean: ___65 ___ Standard Deviation: ___6.14 ___ Your Height: ___66 ___ Please answer the following questions in complete sentences: 1. Discuss your method of collection for the values that you are using in your study (systematic, convenience, cluster, stratified, simple random). For the study, participants were chosen using a convenience sampling method, where individuals who were easily accessible and willing to participate were selected. 2. What are some faults with this type of data collection? One of the main faults with convenience sampling is that it may be representative of only some of the population. This is because individuals who are easily accessible and willing to participate may not be a random sample and may not accurately reflect the characteristics and opinions of the entire population. Additionally, convenience sampling can also introduce bias into the study, affecting the results' accuracy and validity. 3. What other types of data collection could you have used, and how might this have affected your study? Other data collection methods that could have been used include systematic and simple random sampling. Systematic sampling involves selecting every nth participant from a list of the population, while simple random sampling involves randomly selecting participants from the entire population. Using any of these sampling methods could have affected the study differently. For instance, systematic sampling could have been quicker and more accessible, but it may have introduced bias if there was any pattern in the population list. On the other hand, simple random sampling would have been more representative and unbiased than convenience sampling, but it may have been more time-consuming and costly. Calculation of 95% Confidence Interval 1. Give a point estimate (mean) for the average height of all people at the place where you work. What is your point estimate, and what does this mean? The point estimate for the average height of all people in my workplace is 65 inches. It means the sum of each person's height in my workplace and then dividing the sum by the total number of people (20) would equal 65 inches. 2

2. 2. 2. Find a 95% confidence interval for the true mean of heights. What is the interval? [Provide a Screenshot of your work from the t value Confidence Interval for µ from the Confidence Interval tab on the Week 6 Excel spreadsheet] 3. Give a practical interpretation of the 95% confidence interval [ Write a complete sentence] . We are 95% confident that the true population mean height is between 62.13 and 67.87 inches. Calculation of 99% Confidence Interval Now, change your confidence level to 99% for the same data. 1. Find a 99% confidence interval for the true mean of heights. What is the interval? [Provide a Screenshot of your work from the t value Confidence Interval for µ from the Confidence Interval tab on the Week 6 Excel spreadsheet] 4. Give a practical interpretation of the 99% confidence interval [ Write a complete sentence] . We are 99% confident that the true population mean height is between 61.07 and 68.93. Compare Margins of Error 3

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1. Would the margin of error be larger or smaller for the 99% CI? Explain your reasoning. The margin of error for a 99% confidence interval would be larger than the margin of error for a smaller confidence level, such as 95%. A 99% confidence level means we are more confident that the true population parameter falls within the interval. Hence, we need a wider range of potential values to be included in the interval. The more significant margin of error reflects this increased level of uncertainty and provides a wider range of possible values for the true parameter. 2. As the confidence level increases, what happens to the Margin of Error? As the confidence level increases, the margin of error also increases. 4