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lecture23_6slides - Statistics 528 Lecture 23 Confidence...

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Statistics 528 - Lecture 23 1 Statistics 528 - Lecture 23 Prof. Kate Calder 1 Confidence Intervals and Hypothesis Tests in Minitab 1. Use Minitab to get descriptive statistics and then use formulas. 2. Use Minitab directly to compute confidence intervals and perform tests: Stat => Basic Statistics => 1-Sample Z Note: This function is for computing confidence intervals and hypothesis tests of ° , the population mean, assuming the population standard deviation is known. (Section 6.1 and Section 6.2) Statistics 528 - Lecture 23 Prof. Kate Calder 2 Stat => Basic Statistics => 1-Sample Z Variables: enter column of data Sigma: known value of the population standard deviation Test Mean: value of mean under the null hypothesis (H 0 ) Statistics 528 - Lecture 23 Prof. Kate Calder 3 Click on Options box Confidence level: level C of confidence interval or level (1- ± ) of a hypothesis test Alternative: form of alternative hypothesis Not equal => H 0 : ° ² μ 0 Less than => H 0 : ° < μ 0 Greater than => H 0 : ° > μ 0 Note: you need to select not equal as the alternative to calculate an equal tails confidence interval (like the ones we’ve been doing). Statistics 528 - Lecture 23 Prof. Kate Calder 4 t-Tests Previously, when making inferences about the population mean, μ , we were assuming: 1. Our data (observations) are an SRS of size n from the population. 2. The observations come from a normal distribution with parameters μ and σ . 3. The population standard deviation σ is known. Statistics 528 - Lecture 23 Prof. Kate Calder 5 To perform statistical inference, we were using the test statistic (one- sample z statistic): which has a normal distribution. This holds approximately for large samples even if assumption 2 is not satisfied. Why? CENTRAL LIMIT THEOREM n x z σ μ 0 - = Statistics 528 - Lecture 23 Prof. Kate Calder 6 Issue: In a more realistic setting, assumption 3 is not satisfied. That is, ³ is unknown. In more realistic situations where ³ is unknown, we can use the sample standard deviation, s, as an estimate of the population standard deviation, σ . is called the standard error of the sample mean. ° = - - = n i i x x n s 1 2 ) ( 1 1 n s /
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Statistics 528 - Lecture 23 2 Statistics 528 - Lecture 23 Prof. Kate Calder 7 When making inferences about the population mean μ with σ unknown , we use the one-sample t statistic : Note: We are still assuming that assumptions 1 and 2 are satisfied.
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