Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Transcript

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%?