SOLUTION: Hi Stan (U ROCK), I have a couple more I'm having trouble with. THANKS, T F 1. If 40 samples, each of size n=21, were selected from a population of 22,493, we would expect th

Question 138237: Hi Stan (U ROCK), I have a couple more I'm having trouble with. THANKS,
T F 1. If 40 samples, each of size n=21, were selected from a population of 22,493, we would expect the mean of the sample means and the population mean to be close but not exactly equal.
T F 2. A sample of union members was selected and their opinions regarding the proposed management union contract were recorded with 160 out of the 200 members favored the proposed contract. A 95 percent confidence interval for the population proportion ranged from 0. 74 and 0. 85. If the sample were larger, this interval would be larger (wider).

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
T F 1. If 40 samples, each of size n=21, were selected from a population of 22,493, we would expect the mean of the sample means and the population mean to be close but not exactly equal.
True because of the Central Limit Theorem.
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T F 2. A sample of union members was selected and their opinions regarding the proposed management union contract were recorded with 160 out of the 200 members favored the proposed contract. A 95 percent confidence interval for the population proportion ranged from 0. 74 and 0. 85. If the sample were larger, this interval would be larger (wider).
False: The interval would get narrower.
Why?
E = z*(s/sqrt(n))
Since "n" is in the denominator, E gets smaller as n gets larger.
Since the CI is (p-hat - E , p-hat +E) the interval gets smaller
as E gets smaller, as n gets larger.
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Cheers,
Stan H.

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