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χ 2 -test The diameters of ball bearings produced by a certain manufacturer had a variance...

χ 2 -test The diameters of ball bearings produced by a certain manufacturer had a variance of 0.00156. To cut costs, the manufacturer instituted a less expensive production method. A sample of 26 bearings was randomly selected from one week’s production for the new process. The sample variance (for the new method) is 0.0025. (a) (10 points) Utilize the classical approach to perform the following hypothesis test: H0 : σ 2 = 0.00156 versus H1 : σ 2 > 0.00156. Use α = 0.05.

math   Statistics-And-Probability   
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The provided sample variance is s0.0025 and the sample size is given by n 26 (1) Null and Altenative Hypotheses The following null and alternative hypotheses need to be tested: Ho : σ2-0.00156 Ha: 2>0.00156 This corresponds to a right-tailed test, for which a Chi-Square test for one population variance will be used 2) Rejection Region Based on the information provided, the significance level is a0.05, and the the rejection region for this right-tailed test is R-:37.652 (3) Test Statistics The Chi-Squared statistic is computed as follows (n 1)s (26-1) 0.0025 σ. 0.00156 Xt = 40,064

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