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# IE330_Chapter10 - Chapter 10 Homework The due date for this...

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The due date for this homework is 21 February. Read Chapter 10 See Blackboard for homework assignment. Chapter 10: Homework

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You should be able to recall: You should be able to accomplish: Structure comparisons between two samples as hypothesis tests Conduct tests of hypotheses on differences in means between two samples Construct confidence intervals on differences in means between two samples Conduct tests of hypotheses on ratios of the variances of two samples Construct confidence intervals on ratios of the variances of two samples Compute β and power for hypothesis tests on two samples Compute sample size requirements for hypothesis tests on two samples You should be able to understand: The relationship between confidence intervals and hypothesis tests The use of p-values for hypothesis tests Chapter 10: Objectives
In the last chapter we made hypotheses about the parameters of a population, and tested those using a sample. In this chapter we will make hypotheses about the difference in population parameters between two populations, and test those using samples from each population. The method used follows directly from the method we used in Chapter 9. We will again construct test statistics and compare them to critical values of standardized distributions. Example: We want to compare tire wear for tires made using two different formulations. We take a sample of 20 observations of tires made from each formulation (40 total tires), then run them on a test bench for the equivalent of 60,000 miles. We then measure the depth of grooves for each tire. Is there a difference? Chapter 10: Overview

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Example: We want to compare tire wear for tires made using two different formulations. We take a sample of 20 observationsof tires made from each formulation (40 total tires), then run them on a test bench for the equivalent of 60,000 miles. We then measure the depth of grooves for each tire. Is there a difference? Really what we’re asking is: Is the difference in mean tread depth between the two samples = 0? This can be phrased as a hypothesis test about a difference in means: H0: μ 1 - μ 2 = 0 H1: μ 1 - μ 2 ≠ 0 (or μ 1 - μ 2 > 0 or μ 1 - μ 2 < 0) In general, we can test the following: H0: μ 1 - μ 2 = Δ 0 H1: μ 1 - μ 2 ≠ Δ 0 (or μ 1 - μ 2 > Δ 0 or μ 1 - μ 2 < Δ 0 ) Chapter 10: Hypothesis tests on differences in means, variance known
Example: We want to compare tire wear for tires made using two different formulations. We take a sample of 20 observationsmade from each formulation (40 total tires), then run them on a test bench for the equivalent of 60,000 miles. We then measure the depth of grooves for each tire. Is there a difference? In general, we can test the following: H0: μ 1 - μ 2 = Δ 0 H1: μ 1 - μ 2 ≠ Δ 0 (or μ 1 - μ 2 > Δ 0 or μ 1 - μ 2 < Δ 0 ) It can be shown that (page 346) our estimate of a difference in means is normal if the samples are random, the two populations are independent, and both populations are normal.

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IE330_Chapter10 - Chapter 10 Homework The due date for this...

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