Confidence Intervals A1
The confidence interval helps determine the high and low values relating to the estimated population proportion. To compute the confidence interval you will need the critical value. Below you will find a list of some common critical values.
Types of calculations and the formula used depend son the parameter of interest. For example, you can calculate the confidence interval for a population proportion, population mean, difference on population proportions, and difference of population means.
Confidence interval is generally two-tailed and so the critical values are always calculated using the alpha value divided by 2. What determines the direction of the claim is the claim itself. If the claim is that there is no difference or that there is a difference we cannot tell if the claim refers to more than of greater than the parameter of interest. If the claim states that the expected value is either greater than or less than the expected value then we have a one-tail hypothesis test.
The key values you need to know include:
Confidence level Known as the critical value
90% 1.645
95% 1.96
98% 2.33
99% 2.576
Here is an example interpretation statement relating to a confidence interval. Given a 95% confidence level, n = 64, standard deviation = 5 m/g. Confidence interval was calculated to be (26.775 m/g, 28.725 m/g). We are 95% confident that the mean gas mileage for this model of car falls between 26.775 and 28.725.
Within the scope of confidence intervals is the concept of the margin of error which we will explore using the various methods including technology, question stem analysis, formula use, and interpretation. Lets begin to analyze the free response questions relating to confidence intervals and margin of error. Remember that the study guide is ordered and presented according to the order listed in the table of contents.
