B12. Francesca was working with 40 volunteer subjects in a study on opinions about financial risk. She needed to divide these subjects into two groups. The groups were called A and B, and exactly twenty were to be placed in each group. Which of these statements gives the best technique for doing the division?

A. Give the subjects numbers 1 through 40. Then use a computer random number generator to select twenty numbers in the set {1, 2, ..., 40}. The selected numbers identify those in group A. The remaining subjects will constitute group B.

B. For each subject, flip a coin. If the coin lands heads, assign the subject to group A, and if the coin lands tails, assign the subject to group B.

C. Sort the subjects alphabetically by last name. The odd number positions in this list (1, 3, 5, ..., 39) will be group A, and the even number positions (2, 4, 6, ..., 38, 40) will be group B.

D. Group the 40 subjects into twenty pairs. For each of the twenty pairs, flip a coin. If the coin lands heads, make the assignment (A = person first in alphabetical order, B = person second in alphabetical order). If the coin lands tails, make the reverse assignment. For example, if the pair consists of Adamson and Gomez, then heads means (Adamson in group A, Gomez in group B). Tails means (Adamson in group B, Gomez in group A).

B6. An investor bought shares in the five firms whose stocks were the five best Dow Jones companies in the first quarter of the year. In the second quarter, however, the performance of these five firms was rather ordinary. The statistical phenomenon taking place here is

A. The law of averages says that these stocks must perform at the market average over the long haul.

B. The Central Limit theorem says that distributions tend to normal, so that the abnormal results of the previous quarter are difficult to repeat.

C. Statistical independence indicates that performance in the first quarter cannot be used to predict performance in the second quarter.

D. The regression effect says that high performances tend to return to average.

B4. Which of the following statements about the normal distribution is correct?

A. The normal distribution was developed by Dr. Isaac M. Normal.

B. The normal distribution can be used to describe the averages of samples, even if the individual values come from a highly skewed distribution.

C. Every random phenomenon has, at least approximately, a normal distribution.

D. The normal distribution can be used to describe even phenomena like income and corporation earnings, which are highly skewed.

B5. An analyst has tested the statistical hypothesis H0: = 45 regarding the mean of a population. The alternative hypothesis was formulated as H1: 45. The analyst used the 5% level of significance. Based on the data she collected, she rejected H0. This means that:

A. There is at most a 5% probability that = 45.

B. She could not possibly have made a type II error.

C. If she used the 1% level of significance, she still would have rejected H0 in all cases.

D. There is a 95% probability that she would reach the same conclusion with a new set of data.