In 1969, Dr. Spock came to trial before Judge Ford, in Boston\'s federal court h
ID: 3155906 • Letter: I
Question
In 1969, Dr. Spock came to trial before Judge Ford, in Boston's federal court house. The charge was conspiracy to violate the Military Service Act. "On all defendants, Dr. Spock, who had given wise and welcome advice on child rearing to millions of mothers, would have liked women on his jury." The jury was drawn from a "venire," or panel, of 350 persons selected by the clerk jurors in the district were female. At the next stage in selecting the jury to hear the case, Judge Ford chose 100 potential jurors out of the 250 persons. his choices include 9 women. a) 350 people are chosen at random from a large population, which is over 50% female. How likely is it that the sample includes 102 women or fewer? b) 100 people are chosen at random (without replacement) from a group consisting of 102 women and 248 men. How likely is it that the sample includes 9 women or fewer? c) What do you conclude?
Explanation / Answer
A)
Here,
n = 350
p = 0.50
We first get the z score for the critical value:
x = critical value = 102.5
u = mean = np = 175
s = standard deviation = sqrt(np(1-p)) = 9.354143467
Thus, the corresponding z score is
z = (x-u)/s = -7.750576015
Thus, the left tailed area is
P(z < -7.750576015 ) = 4.57383*10^-15 [ANSWER]
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b)
Using a cumulative hypergeometric distribution table or technology, matching
where
N = population size = 350
K = number of successes in the population = 102
n = sample size = 100
x = critical number of successes in the sample = 9
Thus,
P(at most 9 ) = 2.17821*10^-8 [ANSWER]
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c)
It seems like there is discrimination against women here, as we have low probability values.