Inference on Single Mean

Baker department of statistics g university of south

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Unformatted text preview: niversity of South Carolina; Slide 20 University 20 If the time between industrial accidents If follows an exponential distribution with an average of 700 days, what is the probability that the average time between 49 pairs of accidents will be greater than 900 days? accidents G. Baker, Department of Statistics G. University of South Carolina; Slide 21 University 21 XYZ Bottling Company claims that XYZ the distribution of fill on it’s 16 oz the 16 bottles averages 16.2 ounces with a standard deviation of 0.1 oz. We randomly sample 36 bottles and get y = 16.15. If we assume a standard deviation of 0.1 oz, do we believe XYZ’s claim of averaging XYZ claim 16.2 ounces? 16.2 G. Baker, Department of Statistics G. University of South Carolina; Slide 22 University 22 Up Until Now We have been Assuming Up that We Knew the True Standard Deviation (σ), But Let’s Face Facts … Deviation Face When we use s to estimate σ, then the to then calculated value calculated y−µ s/ n follows a t-distribution with n-1 degrees of follows distribution degrees freedom. freedom. Note: we must be able to assume that we are Note: sampling from a normal population. sampling G. Baker, Department of Statistics G. University of South Carolina; Slide 23 University 23 Let’s take another look at XYZ take Bottling Company. If we assume that fill on the individual bottles follows a normal distribution, does the following data support the claim of an average fill of 16.2 oz? 16.1 16.0 16.3 16.2 16.1 16.1 G. Baker, Department of Statistics G. University of South Carolina; Slide 24 University 24 In Summary When we know σ: y−µ Z= σ/ n When we estimate σ with s: with y−µ t df = n −1 = s/ n We assume we are sampling from a normal population. G. Baker, Department of Statistics G. University of South Carolina; Slide 25 University 25 Relationship Between Z and t Relationship Distributions Distributions Z tdf=3 tdf=1 -4 -3 -2 -1 0 1 2 3 4 G. Baker, Department of Statistics G. University of South Carolina; Slide 26 University 26 Internal Combustion Engine The nominal power produced by a studentThe designed internal combustion engine should designed be 100 hp. The student team that designed the engine conducted 10 tests to determine the actual power. The data follow: the 98, 101, 102, 97, 101, 98, 100, 92, 98, 100 Assume data came from a normal distribution. G. Baker, Department of Statistics G. University of South Carolina; Slide 27 University 27 Internal Combustion Engine Summary Data: Column hp n Mean 10 Std. Dev. 98.7 2.9 What is the probability of getting a sample mean of 98.7 hp or less if the true mean is 100 hp? G. Baker, Department of Statistics G. University of South Carolina; Slide 28 University 28 Internal Combustion Engine 98.7 − 100 P ( y ≤ 98.7 | µ = 100) = P t df =9 ≤ = P (t df =9 ≤ −1.418) 2.9 / 10 0.0949 -4 -3 -2 -1 0 1 2 3 4 t(df=9) What did we assume when doing this analysis? G. Baker, Department of Statistics G. Are you comfortable with the assumption?University of South Caroli...
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