An SRS of 16 households is selected in Houston and the numbe

An SRS of 16 households is selected in Houston and the number of remote controls is counted. We are interested in a 99% confidence interval for the population mean number. In the sample, the mean number of remote controls is 7 and the sample standard deviation is s=2.9. Determine the margin of error associated with the confidence interval.

Solution

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    7          
t(alpha/2) = critical t for the confidence interval =    2.946712883          
s = sample standard deviation =    2.9          
n = sample size =    16          
df = n - 1 =    15          
Thus,              
              
Lower bound =    4.863633159          
Upper bound =    9.136366841          
              
Thus, the confidence interval is              
              
(   4.863633159   ,   9.136366841   )

Thus, the margin of error is

E = (upper - lower)/2 = 2.136366841 [answer]