A 99% confidence interval (in inches) for the mean height of a population is 66.

Question

Explanation / Answer

99% confidence interval for the mean height of a population is 66.0< < 67.6

sample size i.e n = 144

sample mean = (lower limit of CI for population mean + upper limit of CI for population mean)/2

= (66+67.6)/2 = 66.8

let sample standard deviation be s

standard deviation of poulation mean = s/n = s/144 = s/12

99% confindence interval is normal distribution is (mean -2.58*sd, mean+2.58*sd)

so 99% confidence interval for the mean height of a population is (66.8-2.58*s/12, 66.8+2.58*s/12)

66.8-2.58*s/12 = 66

2.58*s/12 = 0.8 => s = 12*0.8/2.58 =  3.7209

standard deviation of poulation mean = 3.7209/12 = 0.3101

95% confindence interval is normal distribution is (mean -1.96*sd, mean+1.96*sd)

so 95% confidence interval for the mean height of a population is (66.8-1.96*0.3101/12, 66.8+1.96*0.3101/12) i.e (66.7494, 66.8506)

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