Sample Test 1 (lightbulb case) answers

# Sample Test 1 (lightbulb case) answers - George Mason...

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George Mason University School of Management OM 210: Statistical Analysis for Management Dr. Harvey Singer Sample Problem: Descriptive Statistics Two different brands of 100-watt incandescent light bulbs are being compared, Brand A (national brand) and Brand B (store brand) as to their lifetime (longevity) in continuous usage. Random samples of light bulbs were selected and the bulbs were tested for the lifetimes while continuously lit. The data, in units of whole hours, are presented below. Note that the sizes of the samples are different. Brand A ( n = 20): 684 720 773 831 852 859 870 893 909 922 926 939 943 954 972 997 1005 1016 1052 1080 Brand B ( n = 16) 819 897 907 942 952 986 1012 1017 1026 1032 1048 1067 1096 1101 1119 1133 1. (a) What is the population? All light bulbs made by Brand A and all light bulbs made by Brand B. (b) What is the variable of interest in both samples? Be as complete and specific as necessary. The lifetime of light bulb in hours. (c) What kind of data are reported in both samples? Quantitative, continuous (rounded to whole hours for reporting, so data appear discrete). (d) What is the measurement scale? Be as specific and complete as necessary. Ratio. 2. (a) Determine the sample mean, median, mode and midrange of light bulb lifetime for Brand A. For Brand A, mean = 909.850 hours, median = 924.000 hours, no mode, midrange = 882.000 hours. (b) Determine the sample mean, median, mode and midrange of light bulb © 2010 Harvey A. Singer page 1 of 3

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lifetime for Brand B. For Brand B, mean = 1009.625 hours, median = 1021.500 hours, no mode, midrange = 976.000 hours. 3. (a) Determine the first and third quartiles of the sample data for Brand A. For A, Q1 = 855.500 hours and Q3 = 984.500 hours. (b) Determine the first and third quartiles of the sample data for Brand B. For B, Q1 = 947.000 hours and Q3 = 1081.500 hours. 4. (a) Calculate the sample midquartile and interquartile range of the sample data for Brand A. For A, midquartile = 920.000 hours, IQR = 129.000 hours. (b) Calculate the sample midquartile and interquartile range of the sample data for Brand B. For B, midquartile = 1014.250 hours, IQR = 134.500 hours. 5. (a) Calculate the range, variance, and standard deviation of the sample data for the Brand A sample. For A, range = 396.000 hours, variance = 10791.818 hours^2, standard deviation = 103.884 hours.
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