The following data were drawn from a normal population Find

The following data were drawn from a normal population. Find a 98.6% confidence interval for the mean. 20 12 21 15 22 10 19 20 12 20

Lower confidence level (LCL) = Upper confidence level (UCL) =

Confidence Interval 98.6% of means is equivalent to :

98.6 = ( Sample Mean - 2.4573*std dev /sqrt(n) < Population Mean < Sample Mean + 2.4573*std dev/sqrt(n))

Sample Mean = (20+12+21+15+22+10+19+20+12+20)/10 = 171/10 = 17.1

STD DEV = standard deviation = sqrt(Var)

Var = E(x^2) - E(X)^2 = [(20^2)+(12^2)+(21^2)+.......+(20^2)] / 10 - (17.1^2)

=3099/10 - (17.1^2)

= 309.9 - 292.41 = 17.49

Std Dev = Sqrt(17.49) = 4.1821

Sqrt(n) = Sqrt(10) = 3.16

98.6 = ( Sample Mean - 2.4573*std dev /sqrt(n) < Population Mean < Sample Mean + 2.4573*std dev/sqrt(n))

= (17.1 - 2.4573*(4.1821/3.16) <Population Mean < (17.1 + 2.4573*(4.1821/3.16))

= (13.8178 <Population Mean<20.35)

LCL = 13.8178

UCL = 20.35

Note:

(Sample Mean - Population Mean) follows N(0,1)

Std dev/sqrt(n)