A simple random sample with n 56 provided a sample mean of 23.0 and a sample sta

Question

A simple random sample with n 56 provided a sample mean of 23.0 and a sample standard deviation of 4.3. a. Develop a 90% confidence interval for the population mean (to 1 decimal) b. Develop a 95% confidence interval for the population mean (to 1 decimal). C. Develop a 99% confidence interval for the population mean (to 1 decimal). d. What happens to the margin of error and the confidence interval as the confidence level is increased? - Select your answer - They increase They decrease They stay the same It cannot be determined from the given data The margin of error increases and the confidence interval becomes narrower The margin of error decreases and the confidence interval becomes wider

Explanation / Answer

Mean is 23 and s is 4.3 thus standard error, SE is 4.3/sqrt(56)=0.575

a) For 90% confidence, the z value is 1.65, lower limit which is mean-z*SE=23-0.575*1.65=22.05, upper limit is mean+z*SE=23+0.575*1.65=23.95

b) For 95% confidence, the z value is 1.96, lower limit is mean-z*SE=23-0.575*1.96=21.87 and upper limit is mean+z*SE=23+0.575*1.96=24.13

c) For 99% confidence, the z value is 2.575 lower limit is mean-z*SE=23-0.575*2.575=21.52 and upper limit is mean+z*SE=23+0.575*2.575=24.48

d) Margin or error decreases and confidence interval becomes wider

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