Confidence interval and sample size

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Includes example on how to calculate saple size and confidence interval for mean and population proportion

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NU wants to estimate the mean time spent by its students commuting daily to campus. Thepopulation standard deviation time spend commuting is 8 minutes. A random sample of 49 studentsreveals a mean of 20.5 minutes.a. Construct a 99 percent confidence interval estimate for the population mean time spent by NUstudents commuting daily to campus?b. Within 99 percent confidence, what sample size is needed if NU wants to be within (+/-) 1 minuteof the true population parameter?Please explain and show work (including graphs if necessary).1.Confidence interval = mean EMargin of error (E) = z critical * sigma/ nE = 2.575 *8/ 49E= 2.943Confidence interval = 20.5 2.943=(17.557, 23.4432.N= (Z*/ E)^2N= (2.575* 8/1)^2N= 424.36=4253.NU wants to estimate the proportion of its 1,000 student athletes that play sports during the summerbreak. If a random sample of 100 st
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