A New York Times article entitled \"How Long is Too Long for the Court\'s Justic

Question

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:
Justice Appointed Tenure as of 2005
Rehnquist 1971 34
Stevens 1975 30
O'Connor 1981 24
Scalia 1986 19
Kennedy 1988 17
Souter 1990 15
Thomas 1991 14
Ginsburg 1993 12
Breyer 1994 11

(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. (Round your answer to two decimal places.)

(b) How should we denote the standardized score?
z or t

(c) How should we denote the standardized score if we know the value of the population standard deviation and use it to standardize?
z or t

(d) For 8 degrees of freedom, the probability of a t score being greater than 1.86 is 0.05. Can we reject the hypothesis that these 9 tenures constitute a random sample from a population with mean 15.2?
Yes or No

(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. What would be the results if we used the new sample mean tenure, 14.0, to test if tenure times averaged significantly longer than 15.2 years?
We would surely reject the null hypothesis.
We would surely fail to reject the null hypothesis.

Explanation / Answer

a) (19.6-15.2)/8.1 = 0.54
b) t (because we've estimated the population standard deviation from our sampled data)
c) z
d) No, since 0.54 < 1.86
e) We would fail to reject the null hypothesis since the new mean tenure is less than 15.2, which is consistent with the null hypothesis of the mean being less than 15.2.

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