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Topic: Interval Estimate of a Population Mean and a Population Proportion Based on a sample and a given confidence level, an interval estimate can be developed for a population mean. Here is the formula: x t / 2 s n Below is the procedure to obtain an interval estimate of a population mean using Excel: Function>>category ‘Statistical’>>choose the function ‘Confidence’, which returns the margin error of a confidence interval for a population mean; Next, specify the value of Alpha () – .01, .05, or 0.1, etc >> enter the value of Standard deviation >> enter the sample size. The returned value is the margin of error. To calculate the interval estimate, simply add (subtract) the margin of error to the sample mean to get the upper (lower) limit of the interval estimates. Example: A random sample of 81 checking accounts at a bank showed an average daily balance of $280. The standard deviation of the population is known to be $66. a. Is it necessary to know anything about the shape of the population distribution of the account balances in order to make an interval estimate of the population mean of the account balances? Explain. b. Find the standard error of the sample mean. c. Give a point estimate of the population mean. d. Construct a 90% confidence interval estimate for the mean. e. Construct a 95% confidence interval estimate for the mean. The formula for an interval estimate of a population proportion: p z / 2 p 1 p , n where p is the sample proportion, z / 2 is the z value for a given confidence level, and n is the sample size. Using embedded functions in Excel, we can calculate the upper and lower limits of an interval estimate of a population proportion. The example below is included in the Excel demo for interval estimation: Response Yes No Yes Yes No Interval Estimate of a Population Proportion Sample Size Response of Interest Count for Response Sample Proportion =COUNTA(A2:A901) Yes =COUNTIF(A2:A901,D4) =D5/D3 900 Yes 396 0.44 No No Yes Yes Yes No No Yes No No Confidence Coefficient 0.95 z Value =NORMSINV(0.5+D8/2) Standard Error =SQRT(D6*(1-D6)/D3) Margin of Error =D9*D11 Point Estimate =D5/D3 Lower Limit =D14-D12 Upper Limit =D14+D12 0.95 1.96 0.0165 0.0324 0.44 0.4076 0.4724