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# HW#1 Answer - STAT 20 Spring 2011“ Solution to Homework...

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Unformatted text preview: STAT 20: Spring 2011“ Solution to Homework # 1 (Q1-Q6: 20 marks totai} Note: When the marks for Q7 are added you may end up with a total over 24. This will later count as a bonus. Q2. Text P24 Q2. (3 marks total, 1 for each part). a) You need to consider the number of cars on the road. There were more Corvettes sold in 2002 than Q45’s, so you should look at rates. b) Same issue as in (a), there were more BMW 3-series sold than BMW 7—series. c) FALSE: the rate (2 per 1,000) is low because the denominator is large relative to the numerator. The rate compares the number stolen relative to the number sold. Q2. Text 26 Q7. (4 marks total, 1 for each part). a) This is an observational study so there may be confounding factors. h) Cancer rates increase with age. Women of different marital status have different patterns of sexual activity, and therefore are exposed to different risksa similarly for education. So age, marital status and education are potential confounders. c) Pill—users are sexuaily more active than non—users and may have more partners. That seems to be what makes the rate higher among pill—users. (See Ex 11 011 P23). d) No, see c). Q3. Text Page 53 Q 10. (5 marks total: 2 for part a, 1 for each the others). a} The histogram should look like this, with intervals of equal width. b) In 1880, people did not know their ages and rounded off. c) In 1970, people knew when they were born. d) In 1880, there was a strong preference for even digits (although 4 and 6 lose out to 5) again this is probably due to rounding. In 1970 the preference was much weaker. Q4. TextPSS Q12“ (Emarks) FALSE: There are very few days when the temperature is above 90 degrees. They should have looked at the number of riots divided by the number of days in each temperature range. QS. Text P566 Q4. (3marks) The figure is not a histogram: the class intervals are unequal and the scale on the X—axis does not show this. if you adjust for the lengths of the intervals (as you should) then the pattern goes away as is shown in the picture below. Class intervals include the left endpoint but not the right. For instance, the rectangle whose base is the interval from 25 to 30 represents the students aged 25—29: those aged 30 are in the next rectangle. The ﬁrst rectangle starts at 15 and the last one ends at 75 (somewhat arbitrarily), What the histogram shows is that most students are in their 20’s with a few precocious 10 youngsters ——— and a few determined oldsters! PERCENT PER YEAR m t». 15 25 35 45 55 65 75 we (YEARS) Q6 (from homework, reproduced here in bold): Scores ranged on a test from 19 to 97. in standard units (zmscores) the range was -3.5 to 3. —Sam got an average score, what was his score? -Frodo‘s score in standard units was 1.5. What was Frodo's score? [3 marks: 1 for correct SD, 1 for correct Sam's score (the average), 1 for correct Frodo score. Do not double~pena1ize, deduct 1 for incorrect SD but give points for consistency] The range is (97—19) which is 78 marks. The range in z«terms is (3-—(~3.5)) which is 6.5 (SD’s) So an SD must be equal to 78/65 which is 12 marks. The average is 3813’s below 97 (which has a z—score of 3) so the average is at (97-36) = 61. So Sam scored 61. Frodo had a z—score of 1.5 (which means he was 18 marks above the average) so Frodo got 79. OR: Let the mean be In, the SD he s. 97 = 1n + 3s 19 m In — 3.55 Solving the simultaneous equations for in and 8 gives to = 61, s : 12 as before. Note: When the marks for Q7 are added you may end up with a total over 24. This will later count as a bonus. ...
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