Bowie State University Constructive Confidence Intervals Questions

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Mathematics

Bowie State University

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I need help with my homework. The files will be attached if you have any questions please let me know.

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As a healthcare professional, you will work to improve and maintain the health of individuals, families, and communities in various settings. Basic statistical analysis can be used to gain an understanding of current problems. Understanding the current situation is the first step in discovering where an opportunity for improvement exists. This project will assist you in applying basic statistical principles to a fictional scenario in order to impact the health and wellbeing of the clients being served. You are currently working at Grady Memorial Hospital in the Infectious Diseases Unit. Over the past few days, you have noticed an increase in patients admitted with a particular infectious disease. You believe that the ages of these patients play a critical role in the method used to treat the patients. You decide to speak to your manager and together you work to use statistical analysis to look more closely at the ages of these patients. You do some research and put together a spreadsheet of the data that contains the following information: • Client number • Infection Disease Status you can • Age of the patient You need the preliminary findings immediately so that start treating these patients. So let's get to work!!!! The data set consists of 60 patients that have the infectious disease with ages ranging from 35 years of age to 76 years of age for Grady Memorial Hospital. 1. Discuss the importance of constructing confidence intervals for the population mean. o What are confidence intervals? o What is a point estimate? o What is the best point estimate for the population mean? Explain. o Why do we need confidence intervals? 2. Find the best point estimate of the population mean. 3. Construct two confidence intervals for the population mean: a 95% confidence interval and a 99% confidence interval. Assume that your data is normally distributed and the population standard deviation is unknown. o Please show your work for the construction of these confidence intervals and be sure to format your equations to fit the appropriate form (may need editing here). 4. Write a paragraph that correctly interprets the confidence intervals in context of your selected topic. 5. Compare and contrast your findings for the 95% and 99% confidence intervals. o Did you notice any changes in your interval estimate? Explain. o What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain.2 Give an example of an interval estimate of an average or proportion you may use in your daily life. For instance, you may say that you are pretty sure your average commute time is between 25-30 minutes, or you are fairly confident that between 60-65% of the population love dogs. Collect some data to see how well your intuition is working. First, does your sample data meet all assumptions necessary to construct the confidence interval of the type you need? Even if it doesn't, construct and interpret the confidence interval. Patient # 1 2 3 4 5 6 7 Infectious Disease Yes Yes Yes Yes Yes Yes Yes Yes Yes & 9 Yes 10 11 12 13 14 Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 Age 69 35 60 55 49 60 72 70 70 73 68 72 74 69 46 48 70 55 49 60 72 70 76 56 59 64 71 69 SS 61 70 SS 45 69 54 48 60 61 50 59 60 62 63 53 64 50 69 52 68 70 Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes 45 46 47 48 49 SO 51 52 53 54 55 56 57 58 59 Yes Yes Yes Yes 59 58 Yes Yes Yes Yes Yes 65 61 59 71 71
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Explanation & Answer

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1. Answers:
• Let 𝜃 be a population parameter. If we want to find 𝜃̂1 and 𝜃̂2 such that
𝑃(𝜃̂1 < 𝜃 < 𝜃̂2 ) = 1 − 𝛼, where 𝛼 between 0 and 1, the interval 𝜃̂1 < 𝜃 < 𝜃̂2 which is
computed from the selected sample is called a 100(1 − 𝛼)% confidence interval.
• Let 𝜃 be a population parameter. A single value 𝜃̂ of a statistic 𝜗 of 𝜃 is called a point
estimate.
• The one with the smallest variance is the best point estimate for a population, thus the
sample mean is the best point estimate for the population mean.
• Confidence intervals provide an upper and lower limit around population parameter 𝜃,
so we can be confidence that we have that parameter in our int...


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