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Decreasing the sample size from 750to 375would multiply the standard deviation by

(a) 2.

(b) 2.

(c) 1/2.

(d) 1/2.

(e) none of these.

Short Answer

Expert verified

The correct answer is (b)2.

Step by step solution

01

Given Information

Random sample size, n=750.

The percentage of Division I athletes that believe these drugs are a concern. =30%.

02

Explanation

Consider pthe proportion of Division I athletes who believe these drugs are a problem and nthe sample size.

p=30%

=0.30

n=750

375is half of the sample size of750.

If the sample size is reduced to 375, the sample size is written as n2=375.

03

Explanation

Know what the sampling distribution's standard deviation of p^is p^=p(1-p)n.

For a sample size of 375, write the standard deviation of the sampling distribution as follows:

p^=p(1-p)n2

=2p(1-p)n

=2p(1-p)n

The standard deviation is then multiplied by 2.

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