Statistics Confidence Intervals?

The forced vital capacity of 11-year-old white boys is normally distributed


with variance = 400^2. The average vital capacity of a sample of 19 boys is 2400 cc.


(a) Construct a 95% confidence interval for this population mean.


(b) Give the precision of this interval.


(c) State the probabilistic interpretation of the result.

Statistics Confidence Intervals?
The formula for a t-based confidence interval for the mean is:





xbar + - tcrit (sd)/sqrt(n)





where


xbar = sample mean


tcrit = the critical value from the t-distribution


sd = the standard deviation


n = sample size





In your case we have n= 19 so we have 18 degrees of freedom and the critical t-value (obtained from a table or calculator) is 2.101. Thus we have





a)


CI = 2400 +- (2.101)(400)/sqrt(19)


CI = (2207.2, 2592.8) approximately





b)


One estimate of precision is half the width of the confidence interval: 192.8 approximately.





c)


If we were repeatedly to take samples of 19 boys and calculate the mean of their vital capacities, 95% of the time the mean we calculated would fall within the limits of the confidence interval we just constructed.