Inference on Single Mean

B decrease c remain the same a g baker department of

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Unformatted text preview: he same. A. G. Baker, Department of Statistics G. University of South Carolina; Slide 49 University 49 Interval Width, Level of Confidence Interval and Sample Size and At a given sample size, as level of confidence increases, interval width __________. __________. At a given level of confidence as sample size increases, interval width __________. size G. Baker, Department of Statistics G. University of South Carolina; Slide 50 University 50 Calculate Sample Size Before Calculate Sampling! Sampling! The width of the interval is determined by: The ± zα / 2 σ n Suppose we wish to estimate the mean to a maximum error of e: Max error = e = zα / 2 σ n zα / 2σ n= e 2 G. Baker, Department of Statistics G. University of South Carolina; Slide 51 University 51 Plastic Injection Molding A plastic injection molding process for a part that has a critical width dimension historically follows a normal distribution with a standard deviation of 8. with What sample size is required to estimate the true mean width to within + 2 units at units 95% confidence? 95% What sample size is required to estimate the true mean width to within + 2 units at units 99% confidence? 99% G. Baker, Department of Statistics G. University of South Carolina; Slide 52 University 52 If we don’t have prior knowledge of the have standard deviation, but can assume we are sampling from a normal population… population Instead of using a z-value to calculate the Instead value confidence interval… confidence P (−tα / 2 Y −µ < < +tα / 2 ) = (1 − α ) s/ n P( µ = Y ± tα / 2 s ) = (1 − α ) n G. Baker, Department of Statistics G. University of South Carolina; Slide 53 University 53 Interval Estimate of the Mean Standard Normal t 1-α α/2 -4 -3 df=n-1 -tα/2 -2 -1 0 α/2 1 +tα/2 2 3 4 (1 – α) 100% Confidence Interval G. Baker, Department of Statistics G. University of South Carolina; Slide 54 University 54 Plastic Injection Molding – Plastic Reworded A plastic injection molding process for a part that has a critical width dimension historically follows a normal distribution. historically A recent sample of four yielded a sample mean of 101.4 and sample standard deviation of 8. deviation Estimate the true mean width with a 95% confidence interval. confidence G. Baker, Department of Statistics G. University of South Carolina; Slide 55 University 55 Hypothesis Testing G. Baker, Department of Statistics G. University of South Carolina Combustion Engine The nominal power produced by a student The designed combustion engine is assumed to be at least 100 hp. We wish to test the alternative that the power is less than 100 hp. that Let µ = nominal power of engine. Let QQ plots shows it is reasonable to assume data QQ came from a normal distribution. came Sample Data: n = 10 y = 98.7 s = 2.8694 G. Baker, Department of Statistics G. University of South Carolina; Slide 57 University 57 Combustion Engine (1) State hypotheses, set alpha. (2) Choose test statistic (3,4) Designate critical value for test and draw con...
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