Maths Flashcards
How do we construct a confidence interval around a population mean?
A confidence interval uses sample data to calculate an estimated range of values that is likely to include an unknown population parameter, for example, the mean. The confidence level (in this case 95%) reflects the probability that the confidence interval will contain the true parameter. The formula for the confidence interval of the mean (CI) is:
CI = sample mean ± Z x (SD/√n); SD = standard deviation and n is the sample size.
Note that (SD/√n) is the standard error of the mean (SEM). If the SD is larger, the chance of error is greater; if the sample size is larger, the chance of error in the estimate is less.
The mean is given as 110. To achieve a 95% confidence interval, use a Z-score of 1.96 (or 2.0, to make the calculation easier). The standard deviation (SD) is given as 20 and the sample size is given as 100. Inserting these values into the formula: CI = 110 ± 4, or a range of 106 to 114.
