MATH 225N Week 6 Assignment Understanding Confidence Intervals

MATH 225N Week 6 Assignment:Understanding Confidence Intervals - ExcelCalculate a Confidence Interval for a Proportion - ExcelQuestionIn a random sample of 350 attendees of a minor league baseball game, 184 said that theybought food from the concession stand. Create a 95% confidence interval for theproportion of fans who bought food from the concession stand. Use Excel to create theconfidence interval, rounding to four decimal places.Yes that's right. Keep it up!(0.4734, 0.5780)Answer ExplanationCorrect answers:0.47340.5780The confidence interval for the unknown populationproportion p is (p̂−z⋆p̂(1−p̂)n‾‾‾‾‾‾‾‾‾√,p̂−z⋆p̂(1−p̂)n‾‾‾‾‾‾‾‾‾√). The confidenceinterval can be calculated using Excel.1. Identify α. Click on cell A1 and enter =1−0.95 and pressENTER.2. Thus, α=0.05. Enter the number of successes, x=184, and sample size, n=350, in theExcel sheet in cells A2 and A3. To find the proportion of successes,p̂, click on cell A4and enter =A2/A3 and pressENTER.3. Thus,p̂≈0.5257. Use the NORM.S.INV function in Excel to find z⋆. Click on cell A5,enter =NORM.S.INV(1−A1/2), and pressENTER.4. The answer for z⋆, rounded to two decimal places, is z⋆≈1.96. To calculate the standarderror,p̂(1−p̂)n‾‾‾‾‾‾‾‾‾√, click on cell A6 and enter =SQRT(A4∗(1−A4)/A3) andpressENTER. 5. The answer for the standard error, rounded to four decimal places,isp̂(1−p̂)n‾‾‾‾‾‾‾‾‾√≈0.0267. To calculate the margin of error, z⋆p̂(1−p̂)n‾‾‾‾‾‾‾‾‾√,click on cell A7 and enter =A5*A6 and pressENTER.6. The answer for the margin of error, rounded to four decimal places,is z⋆p̂(1−p̂)n‾‾‾‾‾‾‾‾‾√≈0.0523. The confidence interval for the populationproportion has a lower limit of A4−A7=0.4734 and an upper limit of A4+A7=0.5780.Thus, the 95%confidence interval for the population proportion of fans who bought foodfrom the concession stand, based on this sample, is approximately (0.4734, 0.5780).Calculate a Confidence Interval for a Proportion - ExcelQuestionAlison, the owner of a regional chain of pizza stores, is trying to decide whether to addcalzones to the menu. She conducts a survey of 700 people in the region and askswhether they would order calzones if they were on the menu. 46 people responded "yes."Create a 90% confidence interval for the proportion of people in the region who wouldorder calzones if they were on the menu.Round your answer to four decimal places.Correct! You nailed it.(0.0503, 0.0811)90% confidence interval is (0.0503, 0.0811)Explanation:Given that x = 46 and n = 700Sample proprotionp^ = x/n = 46/700= 0.0657we know that z critical for 90% level is 1.645Confidence interval =p^±z∗((1−p^)∗p^)/n=0.0657±1.645∗((1−0.0657)∗0.0657)/700 =0.0657±1.645∗0. =(0.0503,0.0811)Calculate a Confidence Interval for the Mean, population standard deviation known- ExcelQuestionA company wants to determine a confidence interval for the average CPU time of itsteleprocessing transactions. A sample of 70 random transactions in milliseconds is givenbelow. Assume that the transaction times follow a normal distribution with a standarddeviation of 600 milliseconds. Use Excel to determine a 98% confidence interval for theaverage CPU time in milliseconds. Round your answers to the nearest integer and useascending order