Question 980616
xbar = 8.1
n = 10
s = 4.8
Since n = 10 makes n > 30 false, and because sigma is not known, we use a T distribution. The critical t value is t = 2.262 (at 95% confidence, df = n-1 = 10-1 = 9). Use a <a href="http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">table</a> to find this


The confidence interval is of the form (L,U) where L is the lower limit and U is the upper limit.


Lower Limit (L):
L = xbar - t*s/sqrt(n)
L = 8.1 - 2.262*4.8/sqrt(10)
L = 8.1 - 2.262*1.51789327688082
L = 8.1 - 3.43347459230442
L = 4.66652540769558
L = 4.67


Upper Limit (U):
U = xbar + t*s/sqrt(n)
U = 8.1 + 2.262*4.8/sqrt(10)
U = 8.1 + 2.262*1.51789327688082
U = 8.1 + 3.43347459230442
U = 11.5334745923044
U = 11.53


The 95% confidence interval for mu is (L,U) = (4.67, 11.53)


Note: The confidence interval can also be stated as 4.67 < mu < 11.53. Some books will use plus/minus notation and say *[Tex \LARGE 8.1 \pm 3.43347] where 8.1 is the point estimate (xbar) and 3.43347 is the margin of error.