Statistical Reasoning 90-707
Solutions to Midterm 1

  1.  
    1. Year (current or previous) is the explanatory variable. [Note that "eating healthfully the previous year" isn't the explanatory variable. The data consist of two columns for year (explanatory), each of which has a bunch of yes or no answers to the question about eating healthfully (response).]
    2. (i)
    3. (iii) due to possible conflict of interest. [Note that using only adults isn't a problem, because the claim specifies that it's about adults. Polling people at various times of the year would actually be a good thing, to avoid making a comparison at a particular time that might not be representative.]
  2.  
    1. 23 (average of 8th and 9th values)
    2. (i) [Picture the stemplot rotated with 1 stems on the left and 2 stems on the right; it has a longer left tail.]
    3. (iii) because 1.5 would be too small: it would suggest wins only come within a couple points of 22.1. On the other end, 15 would be too large: none of the data values are this far from the mean.
  3.  
    1. (iii) [comparing proportion in response of interest (actual cigs or not) for the two explanatory groups (tried e-cigs or not)]
    2. (iii) [15/40=0.375 is about 4 times 85/960=0.089]
    3. 100/1000=0.10
    4. (100/1000)(40)=4
    5. 15+25+85=125 [Note that if you just take 100+40 you're counting 15 twice. Also, "how many" is a count, not a proportion.]
  4.  
    1. 7, 13, 19, 25, 31, 37, 43
    2. 31 [The middle 68% are between 19 and 31 so (100%-68%)/2 are on each tail.]
    3. (i) [Because 11 is between 2 and 3 standard deviations below the mean, the percentage below it must be between 2.5% and 0.15%.]
    4. (36-25)/6=1.83
    5. (ii) [because it's 1.83 sds above the mean; we've said that we start to consider a value as unusual when it gets to about 2 sd's away from the mean]
    6. mean - 1.5 sds=25-1.5(6)=16
  5.  
    1. -0.2037+2.0772(3.5)=7.0665
    2. (ii) [the slope]
    3. (iv) [positive square root of 0.9614]
    4. (iii) because South Oakland has a large residual and Regent Square has an extreme X value that puts it in a position to tip the line down to meet it.
    5. (iii) (S in the output)
    6. (i) [The assignment of roles does not affect the correlation but it does affect the regression line.]
    7. (iii) [0.27 and 0.72 would be too small and 7.2 would be too large]
  •  
    1. (ii) [Note that the main summary at the end makes a comparison between those who didn't or did engage in retaliation.]
    2. (ii) because it is summarized with means
    3. (iv)
    4. (iii) because the second paragraph tells us that 195 participants were randomly assigned into 3 conditions. The statement in the 3rd paragraph is just how the reporter chose to summarize key results. This doesn't change the basic study design. [Recall that in a study of infants choosing toys (featured on the practice midterm) there was a mention of no difference between males and females. This tells us that the design incorporated information about whether an infant was a boy or a girl. Likewise, this design incorporated three conditions: control, abusive supervision but no retaliation, abusive supervision with retaliation.
    5. (i) because they are sample means
    6. (i) In other words, the experiment suffers from a lack of realism. The second option isn't problematic because apparently the harming of virtual voodoo dolls still gave the participants some sense of rectifying injustice. Also, it's a good large sample of size 195, and there was indeed a control group.

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