Inferential statistics are generally used to make inferences about the population based on the measurements taken from the sample. Two applications: 1. Estimation 2. Test of Hypothesis point estimate - a single value/number that can be regarded as a sensible value for the population parameter. Interval estimate- an interval of possible values of an unknown population parameter Ex. Parameter μ σ2 Estimator s2 Confidence Interval ◦ A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. Confidence Interval for the Mean μ Case 1. Large sample size n and known variance σ2 Def. If is used to estimate an unknown mean μ with large sample size n and known variance, then we can be (1- α)100% confident the mean will be within 1. Compute a 95% confidence interval for μ when σ= 3.0, = 58.3, and n= 100. 2. Suppose observation on the speed of 50 vehicles yield a sample mean of 65 mph. Assume the standard deviation of vehicle speed is known equal to 6 mph. Determine the 2-sided 99% confidence intervals of the mean speed. Def. If is used to estimate an unknown mean μ with small sample size n and unknown variance, then we can be (1- α)100% confident the mean will be within Example. 1. Compute a 95% confidence interval for μ when s= 3.0, = 55.3, and n= 16. 2. Concrete placed on a structure was cored and the following results were obtained: 3566, 3779, 3887, 3912, 4005 4142, 3405, 3402, 4039, 3372 psi Determine the 95% 2-sided confidence interval of the mean concrete strength. Example 1. How large a sample is needed if we want to be 95% confident that actual average speed of all vehicles will not exceed by 1.5mph? 2. How large a sample is needed if we want to be 98% confident so that true proportion of household subscribed to PLDT will be within 2%?