**1.** Legendary Harvard University statistics professor Frederick Mosteller reported that if you flip a coin in class and ask if anything suspicious is happening, "hands suddenly go up all over the room" after the fifth head or tail in a row, "so there is some empirical evidence that the rarity of events in the neighborhood of .05 begins to set people's teeth on edge." What is the probability that a fairly flipped coin will give either five heads or five tails in a row?

**2.** To see who serves first in their Thursday squash games, Player A spins the racket while Player B guesses whether the racket logo will stop face up or face down. Player B initially believes that there is only a 5% chance that A cheats when he spins the racket. But after A wins the first five times he spins the racket, B isn't so sure. Assuming that A will always win if he cheats and has a 50% chance of winning if he doesn't cheat, what is B's revised probability that A cheats?

**3.** The September/October 2000 Claremont College's Commuter Chronicle reported that, "As of early August, two-thirds, or 8 out of the 12, ozone Health Advisories this year had occurred on weekends." Are these data statistically persuasive?

**4.** Least squares will be used to estimate the model Y = a + bX + e, using annual data for 1991 through 2000. If X = 100 and Y = 100 in 1991 and X = 200 and Y = 200 in 2000, can the least squares estimate of b possibly be negative? Explain your reasoning.

**5.** A French hospital put 412 patients who had suffered one heart attack on a traditional Mediterranean diet (including olive oil, fruit, and bread); the control group consisted of 358 heart-attack patients who were given a recommended low-fat diet. Four of the patients on the Mediterranean diet and 17 of the patients on the low-fat diet suffered a second heart attack during the two years of the study. Is this observed difference substantial and statistically persuasive?

**6.** A test of the null hypothesis that the average Pomona College student
gains 15 pounds during the first year at college surveyed 100 students and obtained
a sample mean of 4.82 pounds with a standard deviation of 5.96 pounds. Explain
why you either agree or disagree with each of these conclusions:

a. "We assumed that the standard deviation of our sample equaled the population standard deviation."

b. "We calculated the standardized z value to be z = -17.08. The two-sided
p value is 2.82 x 10^{-31}. According to Fisher's rule of thumb, our
data are not statistically significant because our p value is considerably less
than 0.05. This indicates that the probability of observing a large difference
between the sample mean and the population mean that the null hypothesis predicts
is greater than 0.05."

c. "Our data strongly indicate that the Freshman 15 is just a myth. However, it must be recognized that we only took one sample of 100 students. Perhaps if we took other samples, our results would be different."

**7.** An ANOVA test obtained an F value of 0.0; what is the P value?

**8.** A study of injuries suffered by Pomona varsity athletes during the years 1980-1995 obtained these data:

Females | Males | |

Basketball | 214 | 344 |

Soccer | 155 | 236 |

Swimming | 161 | 34 |

Tennis | 82 | 82 |

Track | 151 | 233 |

**9.** Five polls completed on November 5, 2000, gave these results:

number surveyed | Bush (%) | Gore (%) | Margin of Error | |

CNN/USA Today/Gallup | 2386 | 47 | 45 | 2 |

IBD/CSM/TIPP | 989 | 48 | 42 | 3 |

ICR | 1000 | 46 | 44 | 3 |

Reuters/MSNBC | 1200 | 47 | 46 | 3 |

VOTER.COM | 1000 | 46 | 37 | 3 |

**10.** Answer this question to Ask Marilyn:

I recently returned from a trip to China, where the government is so concerned about population growth that it has instituted strict laws about family size. In the cities, a couple is permitted to have only one child. In the countryside, where sons traditionally have been valued, if the first child is a son, the couple may have no more children. But if the first child is a daughter, the couple may have another child. Regardless of the sex of the second child, no more are permitted. How will this policy affect the mix of males and females?