Calculate the upper and lower limit for a 95% confidence interval about the mean.
A family wants to reduce its expenditures for personal items like gifts, newspapers, magazines and so forth. A sample of 49 months of receipts yields a mean of $220.00 with a standard deviation of $30.00. They decide to calculate a 95% confidence interval about this mean. Standard error = (standard deviation)/(square root of sample size)
Upper limit (dollars and cents) =
Lower limit (dollars and cents) =
The critical value for a 95% two-tailed confidence interval is 1.96 given that; Standard error = (standard deviation)/(square root of sample size) now, 1.96 x Standard error = 1.96 x 30/√49 =1.96 x 30/7 = 8.4 Upper limit (dollars and cents) = mean + 1.96SE = 220 + 8.4 = $228.40 Lower limit (dollars and cents) = mean - 1.96SE = 220 - 8.4 =  $211.60
