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Lesechka [4]
3 years ago
13

Which of the following estimates at a 95% confidence level most likely comes from a small sample?

Mathematics
1 answer:
dusya [7]3 years ago
7 0
<span>The <u>correct answer</u> is:

A) 60% ± 18%.

Explanation:

In a confidence interval, the margin of error is given by z*(</span>σ/√n<span>), where </span>σ<span> is the standard deviation and n is the sample size.

First we <u>find the value of z</u>:

We want a 95% confidence level; 95% = 95/100 = 0.95.

To find the z-score, we first subtract this from 1:
1-0.95 = 0.05.

Divide by 2:
0.05/2 = 0.025.

Subtract from 1 again:
1-0.025 = 0.975.

Using a z-table, we find this value in the middle of the table. The z-score that is associated with this value is 1.96.

Back to our formula for margin of error, we have 1.96(</span>σ<span>/</span>√n<span>). The larger n, the sample size, is, the larger its square root is. When we divide by a larger number, our answer is smaller; this gives us a smaller margin of error.

This means that if we had a small sample size, we would divide by a smaller number, making our margin of error larger. The largest margin of error we have in this question is 18%, so this is our correct answer.</span>
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