Consider a situation in which a random sample of 1000 U.S. adults is surveyed an
ID: 3129555 • Letter: C
Question
Consider a situation in which a random sample of 1000 U.S. adults is surveyed and each individual is asked whether or not they believe Obama should appoint the next Supreme Court justice. Researchers would like to test the hypothesis that the majority (more than half) of U.S. adults believe Obama should appoint the next Supreme Court justice. If a new random sample of 1000 adults is taken from the same population, explain whether each of the following would change:
(a) The population proportion, p.
(b) The sample proportion, ˆp.
(c) The mean of ˆp.
(d) The standard deviation of ˆp.
(e) The standard error ˆp (used in calculating a confidence interval for p).
(f) The null standard error of ˆp (used in calculating the test statistic)
Explanation / Answer
a)
No change. The population parameters don't change.
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b)
Yes, it could change. Sample statistics vary from sample to sample.
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c)
No change. It is the population proportion. The population parameters don't change.
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d)
No change. It is the population standard error. The population parameters don't change.
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e)
Yes, it could change, as it changes with p^.
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f)
No change. It is dependent on p, the population proportion.