Homework 1 Text Problems

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Purdue University *

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305

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Statistics

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Feb 20, 2024

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Homework 1 – Problems in the Textbook 1.21 A. The two populations studied are mothers that took DES during pregnancy and mothers that did not take DES during pregnancy. B. The data was most likely collected through a survey because the scientist did not manipulate any of the variables. They simply observed an outcome. C. We can use the sample proportion of women that developed abnormalities and use it gauge how many were impacted out of 1,000. (63/3980) * 1000 = ~15.83 women D. The study concluded that mothers that took the drug are 2x as likely to develop abnormalities so to find the likelihood of developing an abnormality while not taking the drug with: (15.8/2) = ~7.9 E. They use relatively large samples to improve the reliability of their conclusions. 1

1.25 A. There are 7 variables within the dataset. B. The Categorical variables are: Make, Model, Recommended, and Owner Satisfaction The quantitative variables are: Overall Score, Overall Miles per Gallon, and Acceleration 2

C. 7 vehicles are recommended out of 15 total vehicles which means we can find the percentage with (7/15) = 0.47 * 100 = 47% D. The average can be found by adding up all miles per gallon data points and dividing by the number of data points overall. (366/15) = 24.4 miles per gallon E. F. Class Intervals Class Boundaries Tally Bars Frequency 7.0-7.9 6.95-7.95 l 1 8.0-8.9 7.95-8.95 lllll 5 9.0-9.9 8.95-9.95 llll 4 10.0-10.9 9.95-10.95 lllll 5 Total 15 3 Yes No 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 8 8.2 Owner Satisfaction

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2.39 A. B. There is an apparent negative relationship between the two variables where the MPG decreases as the Speed increases. 4 20 25 30 35 40 45 50 55 60 65 0 5 10 15 20 25 30 35 40 Fuel Efficiency as Speed Increases Speed (Miles/Hour) MPG (Miles/Gallon)

3.43 A. The mean is $72,342.94 and the median is $66,743.00. B. The mean is close to the median which means that the data has a symmetrical data. C. The range is $100,132.00 and the standard deviation is $23,711.80. D. The 1 st quartile is $56,799.50 and the 3 rd quartile is $81,533.25. E. The upper limit is $97,076.69 and the lower limit is $47,609.19. There are 2 datapoints above the upper limit which are the outliers within this data. The implications are that these points might be the cause of the data being positively skewed. 5

3.53 A. The median return is 13.9. B. 19 companies had a higher return than the average / 50 total companies = 0.38 *100 = 38% C. -13.9, 3.7, 13.9, 30, 117.1 D. The upper limit is 69.45 and the lower limit is -35.75. There is no data below the lower limit but there are 3 outliers above the upper limit. E. 6

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3.59 A. I expect a negative relationship between smoke detectors and deaths from fires due to smoke detectors warning occupants that there is a fire. B. The correlation between the two is – 0.90596. This is a negative correlation as expected. C. 7 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.0 5.0 10.0 15.0 20.0 25.0 Smoke Detector Usage and Deaths from Fire Smoke detectors used % Deaths from fire

6.11 A. p(z<=-1) = .15866 B. p(z>=-1) = 1- .15866 = 0.84134 C. p(z>=-1.5) = 1- .06681 = .93319 D. p(z<=-2.5) = .00621 E. p(0>=z>-3) = 0.49865 8

6.41 A. Z = 65,000 – 53901 / 15,000 = 0.7399 P( Z >= 65,000) = 1 - 0.77035 = 0.2297 B. Z = 65,000 – 51541 / 11,000 = 1.2235 P( Z >= 65,000) = 1 - 0.88877 = 0.11123 C. Z = 40,000 – 51541 / 11,000 = -1.05 P( Z < 40,000) = 0.14686 D. P( Z < X) = 0.01 X = 2.33 * 11000 + 51541 = 77,171 9

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