Marty Rowatti recently assumed the position of director of the YMCA of South Jer

Question

Marty Rowatti recently assumed the position of director of the YMCA of South Jersey. He would like some current data on how long current members of the YMCA have been members. To investigate, suppose he selects a random sample of 40 current members. The mean length of membership of those included in the sample is 8.32 years and the standard deviation is 3.07 years. a. What is the mean of the population? b. Develop a 90 percent confidence interval for the population mean. The previous director, in the summary report she prepared as she retired, indicated the mean length of membership was now

Explanation / Answer

When the population mean is unknown, you use the t test. The values for the interval will depend on the Confidence Interval you want. See below: *For 95% CI --> a = 0.05: Critical Value = ta/2,n-1 = t0.05/2,40-1 = t0.025,39 = 2.023 (by interpolation) xbar ± ta/2,n-1s/vn 8.32 ± (2.023)(3.07)/(sqrt(40)) 8.32 ± 0.98 [7.34,9.30] *For 90% CI --> a = 0.1: Critical Value = ta/2,n-1 = t0.1/2,40-1 = t0.05,39 = 1.685 (by interpolation) xbar ± ta/2,n-1s/vn 8.32 ± (1.685)(3.07)/(sqrt(40)) 8.32 ± 0.82 [7.50,9.14] *For 99% CI --> a = 0.01: Critical Value = ta/2,n-1 = t0.01/2,40-1 = t0.005,39 = 2.709 (by interpolation) xbar ± ta/2,n-1s/vn 8.32 ± (2.709)(3.07)/(sqrt(40)) 8.32 ± 1.31 [7.01,9.63]

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