Sample size of 10 95 confidence interval estimate of mean he

Sample size of 10, 95% confidence interval estimate of mean height with confidence limits equal to 66 and 74 inches. (a) What is the sample mean? (b) What is the sample standard deviation?

Solution

From the data Margin of error = = (Upper-Lower)/2 = (74-66)/2 = 4
a)
Sample Mean = Lower + ME = 66+4 = 70
b)
Margin of Error = Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
Sample Size(n)=10
Margin of Error = Z a/2 * S.D/ Sqrt ( 10)
4 = 1.96 * S.D/ Sqrt ( 10)
S.D = 4 * Sqrt(10)/1.96 = 6.454