Consider a normal population with an unknown population standard deviation. A ra

Question

Consider a normal population with an unknown population standard deviation. A random sample results in 111formula80.mml = 52.25 and s2 = 15.21. Use Table 2. a. Compute the 99% confidence interval for if 111formula80.mml and s2 were obtained from a sample of 8 observations. (Round intermediate calculations to 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval to b. Compute the 99% confidence interval for if 11formula442.mml and s2 were obtained from a sample of 16 observations. (Round intermediate calculations to 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval to c. Use your answers to discuss the impact of the sample size on the width of the interval. The bigger sample size will lead to a larger interval width and therefore a more precise interval. The bigger sample size will lead to a smaller interval width and therefore a more precise interval.

Explanation / Answer

a) ta/2 = 3.499

lower bound = 52.25 - 3.499*sqrt(15.21/8) = 47.43

upper bound = 52.25 + 3.499*sqrt(15.21/8) = 57.07

b) ta/2 = 2.947

lower bound = 52.25 - 2.947*sqrt(15.21/16) = 49.38

upper bound = 52.25 + 2.947*sqrt(15.21/16) = 55.12

c) option 1  The bigger sample size will lead to a smaller interval width and therefore a more precise interval.

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