An example at the end of the section demonstrates the type of exercise you should be able to solve.
(estimate) +/- (reliability coefficient)(standard error)constructing a confidence interval is simply plugging into the formula
To construct a C% confidence interval,
the multiplier z
Confidence Level | zA 95% confidence interval expressed as 4.5 +/- 2.3 can be interpreted as* ------------------------------------ 90% | 1.645 95% | 1.960 99% | 2.576
"I am 95% confident that the population mean is within 2.3 of the sample mean 4.5" or "I am 95% confident that the population mean is between 2.2 and 6.8".
If your sample size is small and noticeably nonnormal, with extreme outliers, or strong skewness apparent in histograms, you should not use the formula in this section for constructing confidence intervals.
The sample size is large enough that it is reasonable to conclude that the shape of the sampling distribution of is approximately normal. From previous studies, it is reasonable to conclude that the standard error of this distribution is = 3.26.
Plugging into the formula gives an answer 114.0 +/- 6.4, where we used 1.96 for z.
This can interpreted as "we are 95% confident that the unknown mean weight of all infants in Boston is between 107.6 and 120.4 ounces".
Bret Larget, larget@mathcs.duq.edu