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In this module you will begin working on Phase 2 of your course project. Continue using the same data set and variables and perform the following analysis: Discuss the importance of constructing confidence intervals for the population mean.What are confidence intervals?What is a point estimate?What is the best point estimate for the population mean? Explain.Why do we need confidence intervals?Based on your selected topic, evaluate the following:Find the best point estimate of the population mean.Construct a 95\% confidence interval for the population mean. Assume that your data is normally distributed and σ, the population standard deviation, is unknown.Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations.Write a statement that correctly interprets the confidence interval in context of your selected topic.Based on your selected topic, evaluate the following:Find the best point estimate of the population mean.Construct a 99\% confidence interval for the population mean. Assume that your data is normally distributed and σ, the population standard deviation, is unknown.Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations.Write a statement that correctly interprets the confidence interval in context of your selected topic.Compare and contrast your findings for the 95\% and 99\% confidence interval.Did you notice any changes in your interval estimate? Explain.What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain. This assignment should be formatted using APA guidelines and a minimum of 2 pages in length. courseproject_2_datasheetanswers1_12_2020.xlsx phase2moduleproject.docx assignment_rubric.pdf confidence_intervals_overview.docx sta3215_course_project_phase_2_2___1_.docx Unformatted Attachment Preview Patient # Age 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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 44 45 68 68 69 69 69 69 69 70 70 70 70 70 71 71 71 71 71 49 50 73 50 64 74 52 65 76 81 53 68 72 54 68 72 55 68 72 55 72 55 73 56 58 59 59 59 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 59 60 60 60 60 60 61 61 61 62 63 64 64 35 45 46 48 48 49 49 1. o o o o 2. o o o o 3. o o o o 4. o o In this module you will begin working on Phase 2 of your course project. Continue using the same data set and variables and perform the following analysis: Discuss the importance of constructing confidence intervals for the population mean. What are confidence intervals? What is a point estimate? What is the best point estimate for the population mean? Explain. Why do we need confidence intervals? Based on your selected topic, evaluate the following: Find the best point estimate of the population mean. Construct a 95\% confidence interval for the population mean. Assume that your data is normally distributed and σ, the population standard deviation, is unknown. Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations. Write a statement that correctly interprets the confidence interval in context of your selected topic. Based on your selected topic, evaluate the following: Find the best point estimate of the population mean. Construct a 99\% confidence interval for the population mean. Assume that your data is normally distributed and σ, the population standard deviation, is unknown. Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations. Write a statement that correctly interprets the confidence interval in context of your selected topic. Compare and contrast your findings for the 95\% and 99\% confidence interval. Did you notice any changes in your interval estimate? Explain. What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain. This assignment should be formatted using APA guidelines and a minimum of 2 pages in length. 1/3/2020 STA3215 Section 01 Inferential Statistics and Analytics - ... Name Statistics Rubric Description Rubric Detail Levels of Achievement Criteria Insu cient Emerging Competency Pro ciency Mastery Correctness 0.00 \% 50.00 \% 75.00 \% 85.00 \% 100.00 \% Less than half of parts of all problems are solved correctly. At least half of the parts of all problems are solved correctly. The majority of parts of all problems are solved correctly. Almost all parts of all problems are solved correctly. All parts of all problems are solved correctly. 0.00 \% 50.00 \% 75.00 \% 85.00 \% 100.00 \% Less than half of the calculations are clearly shown in Excel and have the proper formulas applied. At least half of the calculations are clearly shown in Excel and have the proper formulas applied. The majority of the calculations are clearly shown in Excel and have the proper formulas applied. Almost all calculations are clearly shown in Excel and have the proper formulas applied. All calculations are clearly shown in Excel and have the proper formulas applied. 0.00 \% 50.00 \% 75.00 \% 85.00 \% 100.00 \% Less than half of the explanations, including describing all formulas, are complete and correct. At least half of the explanations, including describing all formulas, are complete and correct. The majority of the explanations, including describing all formulas are complete and correct. Almost all explanations, including describing all formulas, are complete and correct. All explanations, including describing all formulas, are complete and correct. Weight 25.00\% Work Shown Weight 25.00\% Explanations Weight 25.00\% https://learning.rasmussen.edu/webapps/rubric/do/course/manageRubrics?dispatch=view&context=course&rubricId=_59428_1&course_id=_59928_1 1/2 1/3/2020 STA3215 Section 01 Inferential Statistics and Analytics - ... Levels of Achievement Criteria Insu cient Emerging Competency Pro ciency Mastery Formatting 0.00 \% 50.00 \% 75.00 \% 85.00 \% 100.00 \% Less than half of the equations, expressions, and variables are properly formatted using the equation editor tool in Microsoft Word. At least half of the equations, expressions, and variables are properly formatted using the equation editor tool in Microsoft Word. The majority of equations, expressions, and variables are properly formatted using the equation editor tool in Microsoft Word. Almost all equations, expressions, and variables are properly formatted using the equation editor tool in Microsoft Word. All equations, expressions, and variables are properly formatted using the equation editor tool in Microsoft Word. Weight 25.00\% View Associated Items Print Close Window https://learning.rasmussen.edu/webapps/rubric/do/course/manageRubrics?dispatch=view&context=course&rubricId=_59428_1&course_id=_59928_1 2/2 Confidence Intervals Overview • Confidence Intervals o A confidence interval is a range of values used to estimate a population parameter. They are made by using a point estimate obtained from a sample and then calculating a margin of error about that point estimate. o The point estimate is a single value used to estimate a population parameter. Each parameter type has its own best point estimate statistic. o Margins of error are computed differently depending on the population parameter being estimated. o A confidence level (1 − 𝛼) is the probability that the results of our construction of the confidence interval will contain the population parameter. This Wikipedia article has a good summary of interpretations with some common misinterpretations. • Constructing Confidence Intervals for a Population Proportion 𝒑. o Best point estimate: 𝑝̂ = 𝑥 𝑛 o Critical Value: 𝑧𝛼⁄2 ▪ =NORM.S.INV(1-alpha/2, TRUE) o Margin of Error: 𝐸 = 𝑧𝛼⁄2 √ o Confidence Interval: 𝑝̂ − 𝐸 < 𝑝 < 𝑝̂ + 𝐸 𝑝̂ 𝑞̂ 𝑛 • Constructing Confidence Intervals for a Population Mean 𝝁. o Best Point Estimate: 𝑥̅ o Critical Value: 𝑡𝛼⁄2 ▪ =T.INV(1-alpha/2, n-1, TRUE) o Margin of Error: 𝐸 = 𝑡𝛼⁄2 𝑠 √𝑛 o Confidence Interval: 𝑥̅ − 𝐸 < 𝜇 < 𝑥̅ + 𝐸 • Constructing Confidence Intervals for a Population Standard Deviation 𝝈. o Best Point Estimate: 𝑠 o Left Critical Value: 𝜒𝐿2 (Chi-squared left) ▪ =CHISQ.INV(alpha/2, n-1, TRUE) o Right Critical Value: 𝜒𝑅2 (Chi-squared right) ▪ =CHISQ.INV.RT(alpha/2, n-1, TRUE) o Confidence Interval: √ • (𝑛 − 1)𝑠 2 (𝑛 − 1)𝑠 2 √ < 𝜎 < 𝜒𝑅2 𝜒𝐿2 Finding Minimum Sample Size o For a Population Proportion ▪ If 𝑝̂ is known: 2 [𝑧𝛼⁄2 ] 𝑝̂ 𝑞̂ 𝑛= 𝐸2 ▪ If 𝑝̂ is unknown: 2 [𝑧𝛼⁄2 ] . 25 𝑛= 𝐸2 o For a Population Mean ▪ When 𝜎 is known: 𝑛=[ ▪ 𝑧𝛼⁄2 ∙ 𝜎 2 ] 𝐸 When 𝜎 is unknown: 𝑛=[ 𝑧𝛼⁄2 ∙ 𝑠 2 ] 𝐸 STA3215 Course Project Phase 2 Our next phase of analysis will be to construct confidence intervals that will give us an estimated range of where the true average height of all of my family members lies. A confidence interval is defined as redacted. It is comprised of two components, a point estimate and a margin of error. A point estimate is a redacted. The best point estimate to use for a population mean is redacted. Confidence intervals are useful tools because redacted (instructor note: it is up to you find the information that goes in the redacted portions). Our first confidence interval will use a confidence level of 95\%, that means we will use a value of 𝛼 = 0.05. The sample mean we found in phase 1 is: 𝑥̅ = 67.5758 . We find the critical value with the Excel formula: =T.INV(1 − 𝛼⁄2 , 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 𝑜𝑓 𝑓𝑟𝑒𝑒𝑑𝑜𝑚) = T.INV(0.975, 32). Thus, we get the critical value of: 𝑡𝛼⁄2 = 2.0369 Next, we find the margin of error with the formula: 𝐸 = 𝑡𝛼⁄2 𝑠 √𝑛 = (2.0369) 3.6489 √33 = 1.2938 And now we can find the upper and lower bounds of the confidence interval with the formula: 𝑥̅ − 𝐸 < 𝜇 < 𝑥̅ + 𝐸 67.5758 − 1.2938 < 𝜇 < 67.5758 + 1.2938 66.2819 < 𝜇 < 68.8696 Therefore, we conclude that the true average height (𝜇) for my family is between 66.2819 inches and 68.8696 inches. Technically speaking, if we were to repeat this experiment with the same sample size we would expect the sample mean (𝑥̅ ) to be within this range 95\% of the time. Now we will repeat this process but use a confidence level of 99\%, so that changes our value of alpha to 0.01. The sample mean we found in phase 1 is: 𝑥̅ = 67.5758 . We find the critical value with the Excel formula: =T.INV(1 − 𝛼⁄2 , 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 𝑜𝑓 𝑓𝑟𝑒𝑒𝑑𝑜𝑚) = T.INV(0.995, 32). Thus, we get the critical value of: 𝑡𝛼⁄2 = 2.7385 Next, we find the margin of error with the formula: 𝐸 = 𝑡𝛼⁄2 𝑠 √𝑛 = (2.7385) 3.6489 √33 = 1.7394 And now we can find the upper and lower bounds of the confidence interval with the formula: 𝑥̅ − 𝐸 < 𝜇 < 𝑥̅ + 𝐸 67.5758 − 1.7395 < 𝜇 < 67.5758 + 1.7395 65.8363 < 𝜇 < 69.3152 Therefore, we conclude that the true average height (𝜇) for my family is between 65.8363 inches and 69.3152 inches. Technically speaking, if we were to repeat this experiment with the same sample size we would expect the sample mean (𝑥̅ ) to be within this range 99\% of the time. Upon review, we find that the redacted confidence interval is the wider of the two. This is because redacted (instructor note: it is up to you find the information that goes in the redacted portions). ... Purchase answer to see full attachment