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Unformatted text preview: 1 Chapter 7 Section 7.1: Inference for the Mean of a Population Section 7.2: Comparing Two Means Learning goals for this chapter: Understand what inference is and why it is needed. Know that all inference techniques give us information about the population parameter. Explain what a confidence interval is and when it is needed. Calculate a confidence interval for the population mean when the population standard deviation is unknown. Know the assumptions that must be met for doing inference for the population mean when the population standard deviation is unknown (robustness) for 1- sample mean, matched pairs, and 2-sample comparison of means. Know how to write hypotheses, calculate a test statistic and P-value, and write conclusions in terms of the story. Draw Normal curve pictures to match the hypothesis test. Understand the logic of hypothesis testing and when a hypothesis test is needed. Use the confidence interval to perform a two-sided hypothesis test. Explain sampling variability and the difference between the population mean and the sample mean. Explain the difference between the population standard deviation and the sample standard deviation. Know which technique is most appropriate for a story: confidence interval, hypothesis test, or simple summary statistics. Know which inference technique is most appropriate for a story: 1-sample mean using Z, 1-sample mean using t, matched pairs, or 2-sample comparison of means. Interpret Normal quantile plots and histograms to determine whether the t procedures are appropriate. Know how to do all calculations (listed above) by hand with the t table and using SPSS. In Chapter 6 , we knew the population standard deviation . Confidence interval for the population mean : * X x z n Hypothesis test statistic for the population mean : / x z n Used the distribution ~ ( , ) x N n . 2 In Chapter 7 , we don’t know the population standard deviation Use the sample standard deviation ( s ) Confidence interval for the population mean : * s x t n Hypothesis test statistic for the population mean : / x t s n t distribution uses n-1 degrees of freedom. Sometimes you’ll see the symbol for standard error: ˆ x s n Using the t-distribution : Suppose that an SRS of size n is drawn from a N ( , ) population. There is a different t distribution for each sample size, so t(k) stands for the t distribution with k degrees of freedom. Degrees of freedom = k = n – 1 = sample size – 1 As k increases, the t distribution looks more like the normal distribution (because as n increases, s ). t(k) distributions are symmetric about 0 and are bell shaped, they are just a bit wider than the normal distribution. Table shows upper tails only, so o if t * is negative, P(t < t * ) = P(t > |t * |) ....
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- Spring '08
- Normal Distribution, Sig.