Inference about Population Mean we will discuss both estimation and hypothesis testing confidence intervals for μ: work from Figures 5.1 and 5.2 to see that a 95% confidence interval for μ is ybar ± moe where moe=1.96(σ/sqrt(n)) . NOTE: this assumes that σ is known! go to R#4 to simulate the 50 confidence intervals and reproduce Figure 5.3 on p. 177. p

What if the moe is too large for the estimation you want? What happens if you change the level of confidence? Look at Figure 5.4 to see the general method for computing the moe - the R function qnorm(1-α/2) will get the zα/2 you need… What if the moe is too large for the estimation you want? change the level of confidence or change the sample size so, for a specific moe you want, say E: set E= zα/2 (σ/sqrt(n)) and solve for n (note everything else in the equation is known. HW: Read through top of p.192 (stop at ‘computing beta’); work 5.4, 5.5, 5.9, 5.12, 5.13, 5.16(a,b), 5.19, 5.22, 5.23(a,c),5.24-5.26. p

Statistical Tests for μ: try to see what n would be for smaller and smaller E using R and the formula on p.183: E=seq(3.6,.1,by=-0.5)#sequence from 3.6 down to .1 n=(1.96*10/E)^2 #95% confidence, with sigma=10 Statistical Tests for μ: set up the null and research hypotheses in terms of the population parameter μ H0 and Ha give the test statistic you’ll use to decide between the two hypotheses (write TS) set up the rejection region (RR) in terms of the TS under the assumption H0 is true do computations, draw conclusions - context! p

evaluate the error probabilities associated with the decision: Type I error: rejecting a true null hypothesis. The probability of a Type I error is denoted by α Type II error: accept a false null hypothesis. The probability of a Type II error is denoted by β see Table 5.3 on page 187 specify α to set up RR - depends upon the alternative hypothesis (one-sided vs. two- sided) see the box at top of page 191 showing a summary of the Statistical Test for μ of a Normal Population with σ known. HW: p. 199ff #5.16(a,b), 5.19, 5.22, 5.23(a,c) p