10.1 – Estimating with Confidence

Recall: The Law of Large Numbers says the sample mean from a large SRS will be close to the unknown population mean µ. The CLT tell us that the mean of sampling distribution is close to normal. The standard deviation of the sampling distribution is: Empirical Rule:

Confidence Intervals A level C confidence interval for a parameter has two parts: – An interval that is calculated from the data, in the form: Estimate +/- margin of error – A confidence level C, which gives the probability that the interval will capture the true parameter value in repeated samples.

Conditions for Constructing a Confidence Interval for µ Data from a SRS from the population of interest. The sampling distribution of is approximately normal. – Either population is approximately normal or n is large enough.

Confidence Interval for a Population Mean SRS of size n from a population having unknown mean µ and known standard deviation σ. A level C confidence interval for µ is: z* is the value with area C between –z* and z* under the standard normal curve. – z* is called the critical value.

4 Steps for Confidence intervals 1: Identify the population of interest and the parameter you want to draw conclusions about. 2: Choose an appropriate inference procedure. Verify the conditions for the selected procedure. 3: If the conditions are met, carry out the inference procedure. – CI = estimate +/- margin of error. Interpret your results in the context of the problem.