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Math 146 – Introductory Statistics –- Fall 2014 Name: __________________________________ Due Nov 3, 2014 Please do/show all work (neatly !) on this sheet (there are printers available on campus) 1. A sample (n=100) of cereal boxes are examined. The average weight of the boxes is 15 oz.; the standard deviation is 0.3 oz. A ‘promotional item’ that weighs exactly (!) 2 oz. is placed in each box. Now what is the mean weight? What is the standard deviation of weight? (or, is more information needed to answer the question?) Explain. 2. Data set A: 20, 32, 15, 27, 16 a) Find the mean (µ) of data set A b) Subtract the mean (from step “a”) from each data value in set A, to create a new data set “B” c) Find the mean of data set B d) Complete: If one subtracts the mean from each value in a data set, the resulting values have a mean of _________. e) Without doing any calculations, how does the standard deviation of set A compare to the standard deviation of set B? Explain. 3. Data set C: 3, -1, 5, 3, 5, 3 a) Find the z-score for each value in data set C. This creates a new data set D. b) Find the mean (µ) of data set D c) Find the standard deviation of data set D d) Any conclusion? Explain. (Is your conclusion true for all datasets?) 4. Jack (in his first week of statistics class) and Jill (in her eighth week of class) were writing up the results of a statistical study. They reported a sample size of 22 with a mean value of 18.75. When organizing their papers to write the summary, they found the report for another observation. It states a value of 3.80 for the variable under consideration (all other original paper work for the other subjects had been lost). Jack: ”How can we report the correct mean value – we don’t have all the data to add up?” Jill: “All you have to do is _________” What was Jill’s plan and method? And what is the corrected value of the mean? 5. In a similar study Ben and Jerry were compiling results. Ben: “We got a value of 65.40 for the standard deviation.” Jerry: “Are you sure that’s correct? You understand that this is a sample of size 25 and not a population, right?” Ben: “Oops! I thought we were computing for the population. We lost the original data (there’s a lot of bad science going around...), so how do we report the corrected standard deviation?” Jerry: “All you have to do is ____”. What was Jerry’s plan and method? And what is the corrected value of the standard deviation?