# Chap12-Inference-About-a-Population - 1 Chap 12 Inference...

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1 CHAPTER 12: INFERENCE ABOUT A POPULATION Stats & Prob. for Bus. Mgmt (Stat1100) Jochem Chap 12: Inference about a Pop. b Goals of Chapter 12 Be able to do inference* about … b 1. a Population Mean when the Std Dev is unknown . . a Population Variance. 2 b 2. a Population Variance. b 3. a Population Proportion. s Selecting the right sample size to estimate a population proportion with a given margin of error. * i.e. computing an interval estimate and testing a hypothesis b 1. Interval Estimator for Population Mean b In Chap 10, we introduced the interval estimator: 3 Chap 12: Inference about a Pop. s This estimator assumes that we do know the standard deviation of the population, σ. In reality, however, we usually don’t know σ. b 1. Interval Estimator for Population Mean b With a slight change we can modify the interval estimator to work also when we do not know the standard deviation: 4 Chap 12: Inference about a Pop. s where s is now the sample standard deviation, and s t is the t -statistic (the number of sample std dev. from mean)

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1. Interval Estimator for Population Mean b The t-statistic is (or t-test statistic) is just like the z-(test) statistic the number of std. dev. away from the mean. s Before: # of population std dev; now: # of sample std dev. 5 Chap 12: Inference about a Pop. s 1. we replaced σ with the sample std deviation “ s s 2. t-statistic: s z-statistic : std. normally distr. ; we use Table 3 to look up values. s t-statistic: Student t distributed, i.e. we now need to look up values in Table 4. 6 Chap 12: Inference about a Pop. b 1. Interval Estimator for Population Mean b Recall: the Student t distribution is bell-shaped and has only one parameter, the “degrees of freedom ν ( pronounced: nu), which equals the sample size minus 1. s When ν goes to infinity, the Student t distribution becomes the Normal distribution. In general however, the Student t distribution is flatter (i.e. has a greater spread) than the normal distribution. 7 Chap 12: Inference about a Pop. b 1. Interval Estimator for Population Mean b How to look up values in Table 4? s Example: look up the t-statistic for a sample size of 30 when the significance level is 5% and it’s a right-tail test. . Sample size = n = 30 s 1. Sample size = n = 30 B degrees of freedom ν = n-1=29. s 2. Locate “29” as the degree of freedom (df) in Table 4 s 3. Go to the column where it says t 0.050 . B t ν =29,0.050 =1.699. Example 8 Chap 12: Inference about a Pop. b 1. Interval Estimator for Population Mean b Example1: Q12.24 (p393) s A federal agency responsible for enforcing laws governing weights and measure routinely inspects packages to determine whether the weight of the contents is at least as great as that advertised on the package. A random sample of 18 containers whose packaging states that the contents weigh 8 ounces was drawn. Its sample mean is 7.91 ounces and the sample standard deviation is 0.085. s
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Chap12-Inference-About-a-Population - 1 Chap 12 Inference...

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