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3 November, 00:54

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

A. 60% (±18%)

B. 62% (±6%)

C. 65% (±2%)

D. 71% (±4%)

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Answers (1)
  1. 3 November, 01:08
    0
    The correct answer is:

    A) 60% ± 18%.

    Explanation:

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

    First we find the value of z:

    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 (σ / √n). 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.
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