1. In the 1920s, a vaccine called BCG was tested to see if it could reduce deaths from tuberculosis [12]. A group of doctors gave the vaccine to children from some tubercular families and not to others, apparently depending on whether parental consent could be obtained easily.

Over the subsequent 6-year period, 3.3% of the unvaccinated children and 0.67% of the vaccinated children died from tuberculosis. A second study was then conducted in which doctors vaccinated only half of the children who had parental consent, using the other half as a control group. This time 1.42% of the unvaccinated children and 1.52% of the vaccinated children died from tuberculosis. Provide a logical explanation for these contradictory findings.
2. The daughters of women who immigrate to the United States have more upward economic mobility than the daughters of women born in the United States, suggesting that US women have less economic mobility than women in other countries. Identify the most important statistical bias in this sample.
3. A drinker consumes more than twice as much beer if it comes in a pitcher than in a glass or bottle, and banning pitchers in bars could make a dent in the drunken

Driving problem, a researcher said yesterday. Scott Geller, a psychology professor at Virginia Polytechnic Institute and State University in Blacksburg, Va., studied drinking in three bars near campus. [O]n average, bar patrons drank 35 ounces of beer per person when it came from a pitcher, but only 15 ounces from a bottle and 12 ounces from a glass.
4. Do you think that the probability distribution of household income in the United States is skewed left, skewed right, or symmetrical? If a random sample of 100 households is taken, do you think that the sampling distribution of the sample mean is skewed left, skewed right, or symmetrical?

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Table 5.3 Exercise 5.6 Median Weekly Eamings in 2011 Unemployment Rate in 2011 Doctoral degree Professional degree Master's degree Bachelor's degree Associate's degree Some college, no degree High school diploma No high school diploma 2.6% $1551 2.4% $1665 3.6% $1263 4.9% $1053 6.8% $768 8.7% $719 9.4% $638 $451| 14.1% Table 5.4 Exercise 5.17 Month Married Fraction of Divorces Month Married Fraction of Divorces July August September October November December 0.087 January February March April May June 0.064 0. 103 0.067 0.073 0.080 0.090 0.078 0.079 0.087 0.117