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## Chapter 3 Cumulative Test

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**Chapter 3 Cumulative Test**Sample 30 people spent on books ($) 156 150 109 98 136 170 178 195 110 191 187 119 104 160 132 117 111 120 103 123 153 91 162 93 118 127 90 181 110 116**1) qualitative or quantitative and level of measurement**• Data is quantitative • Data is ratio (there is a true 0)**2) Method of data collection. Sampling technique**• Use a survey • Collect data using random sampling (randomly chosen people) • If data were systematic or convenience the sample might not be representative of the amount people spent on boods.**3. Make frequency distribution with 5 classes. Include class**limits, midpoints, frequencies, boundaries, relative freq and cumulative freq.**Stem and leaf**• 9 : 0138 • 10 : 349 • 11 : 0016789 • 12 : 037 • 13 : 26 • 14 : • 15 : 036 • 16 : 02 • 17 : 08 • 18 : 17 • 19 : 15**Mean median and mode**• Mean= $133.67 • Median= $121.50 • Mode = $100.50 • These are statistics because they describe a sample**Range, variance and standard deviation**• Range = $195 -90 = $105 • Variance = 1040.5 • standard deviation = $32.26 • The range is larger than 3 standard deviations.**Probability spending < $120**• Frequency estimate = 14/30= .467 • Prob randomly selecting person who spent more than $120. There are 15 such people in the sample. So Prob=0.5**Prob person spent < $120 or > $160**• These are mutually exclusive events (person cannot do both). So the probability is the sum of the probabilities of individual events which is 14/30 + 7/30 = 21/30 = .7**5 person sample. Prob (at least one spent > $175)**• Pr(any person spent > $175) = 5/30 = .1667 • Pr(at least 1 person spent > $175) = 1 - Pr(no people spent > $175) • Assume samples are independent (i.e not from the 30 people sampled, which would be a dependent sample • Pr(one person > $175) = .8333 • Pr(1 or more) = 1 - .833^5 = .598 • If dependent then = 1 - 25*24*23*22*21/(30*29*28*27*26) = .627**How many ways can 5 respondents be resampled from 30?**• Order is not important so it is number of combinations of 30 things taken 5 at a time • This is 142506