For Discussion At the end of the first two weeks of the baseball season, newspapers start publishing the top ten batting averages. The leader after the first two weeks normally has a batting average of .450 or higher. Yet no major league baseball player has ever finished the season with a better than .450 average. What do you think is the most likely explanation for the fact that batting averages are higher early in the season?

Imagine that you are a golfer of above-average ability and that you have the opportunity to play the greatest golfer in the world (say Phil Mickelson). If you want to maximize your slim chance of winning, how much golf would you elect to play, given the choices of 1, 18, 36, or 72 holes?

A certain town is served by two hospitals A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. Although the overall proportion of boys is about 50 percent, the actual proportion at either hospital may be greater or less than 50 percent on any day. At the end of a year, which hospital will have the greater number of days on which more than 60 percent of the babies born were boys? (a) the larger hospital (b) the smaller hospital (c) neither—the number of days will be about the same (within 5 percent of each other)

The smaller hospital will have many more days of 60 percent boys The smaller hospital will have many more days of 60 percent boys. In fact, the smaller hospital will have 55 such days a year, on the average, while the large one will have only 27.

Imagine an urn filled with white and black balls. You know that two-thirds of the balls are one color and one-third are the other, but you don’t know which color predominates. One blindfolded person plunges a hand into the urn and comes up with 3 black balls and 1 white ball. Another uses both hands and comes up with 14 black balls and 10 white balls. Which sample provides the more convincing evidence that the urn contains more black balls than white balls? (a) the first, or 3:1 sample (b) the second, or 14:10 sample (c) they are equally convincing

Most people will find the smaller sample more compelling, since the black balls are in the majority by a three-to-one margin, whereas the larger sample has only a little more than half black balls. Nevertheless, in terms of probability theory, the latter provides the more convincing evidence. The odds that it accurately indicates the majority color in the urn are 16 to 1. The odds that the smaller sample does are only 4 to 1. Emphasize that the failure to consider sample size leads people to be too confident of exact percentage results from small numbers and not trusting enough of percentage results from large, representative samples.

The personnel manager of a large firm had to select a new chief accountant. No one in the firm’s accounting office was qualified for the job, so an outside candidate had to be found. The job requirements were expertise and practical experience in accounting, organizational skills, and the ability to get along with and to lead other people. There were two candidates for the job: Mr. Simpson and Mr. Barker. Each had worked for a small firm previously, and they had about the same amount of experience in accounting. Both had letters of Recommendation from two former employers. The personnel manager personally knew all the employers and trusted their judgment. Both letters on Mr. Simpson indicated that he was an excellent accountant and that his Organizational skills (delegation of responsibility, regulation of paper flow, meeting deadlines) were fairly good. One letter said he was a fairly effective leader, but he did not get along with several members of his staff and, in fact, some actively disliked him. The other letter also expressed some fairly strong reservations about his ability to get along with the staff, but not about his leadership ability. Both letters on Mr. Barker indicated that he was an excellent accountant and that his organizational skills were quite good. Both letters stressed that he was an excellent leader and that he got along extremely well with almost all staff members. The personnel manager interviewed both men and introduced them to the twelve-member accounting staff at a half-hour get- acquainted session. Mr. Simpson seemed quite impressive, obviously intelligent, energetic, and good humored. He made a very solid impression on the personnel manager and on most of the staff members. Mr. Barker did not make such a good impression, either on the personnel manager or on the staff. He seemed intelligent enough, but somewhat ill-at ease and awkward. Most of the staff wondered how easy he would be to get to know and to communicate with. Which candidate should the personnel manager pick and why? What are the most important things to take into consideration?