A New York Times article entitled "How Long is Too Long for the Court's Justices?" reported in 2005 that the average Supreme Court justice between 1789 and 1970 served for 15.2 years. More recently, tenures tended to be longer, with the following times for the 9 justices serving in the first half of 2005:
a. The mean tenure (in years) was 19.6 and the standard deviation was 8.1. Find the standardized tenure score, if these 9 were a random sample of tenures taken from a population with mean 15.2.
b. Explain why the standardized score should be written t and not z.
c. What information would be needed if we want to report a z statistic for the standardized score?
d. For 8 degrees of freedom, the probability of a t score being greater than 1.86 is 0.05. Explain why we cannot reject the hypothesis that these 9 tenures constitute a random sample from a population with mean 15.2.
e. By the second half of 2005, Rehnquist died and was replaced by Roberts; O'Connor retired, and was replaced in early 2006 by Alito. Explain why the new sample mean tenure, 14.0, could not be used as convincing evidence that tenure times averaged significantly longer than 15.2 years.