a 99% confidence inter for mean height in inches of apopulation is 65.2< and <66

Question

a 99% confidence inter for mean height in inches of apopulation is 65.2< and <66.8 based on a sample size of 144constructing a 95% confidence interval -find sample mean and sample standard deviation -use values to calculate 95% confidence interval a 99% confidence inter for mean height in inches of apopulation is 65.2< and <66.8 based on a sample size of 144constructing a 95% confidence interval -find sample mean and sample standard deviation -use values to calculate 95% confidence interval

Explanation / Answer

The 99% CI is (65.2, 66.8) =0.01, Z(0.005)=2.58 (check normal table) n=144 the sample mean is (66.8+65.2)/2 = 66 the sample standard deviation is 3.72 xbar - Z*s/n = 66 - 2.58*s/sqrt(144) =65.2 --> 0.8= 2.58*s/sqrt(144) --> s= 0.8*sqrt(144)/2.58 = 3.72 --------------------------------------------------------------------------------------------- =0.05, Z(0.025)=1.96 (check normal table) The 95% CI is xbar ± Z*s/n --> 66 ± 1.96*3.72/sqrt(144) --> (65.39, 66.61)

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