A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in her district.
A) If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.
B) If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

(A) The minimum sample size required achieve the margin of error of 0.04 is 601.

(B) The minimum sample size required achieve a margin of error of 0.02 is 2401.

Step-by-step explanation:

Let us assume that the percentage of support for the candidate, among voters in her district, is 50%.

(A)

The margin of error, MOE = 0.04.

The formula for margin of error is:

The critical value of z for 95% confidence interval is:

Compute the minimum sample size required as follows:

Thus, the minimum sample size required achieve the margin of error of 0.04 is 601.

(B)

The margin of error, MOE = 0.02.

The formula for margin of error is:

The critical value of z for 95% confidence interval is:

Compute the minimum sample size required as follows:

Thus, the minimum sample size required achieve a margin of error of 0.02 is 2401.

answer: 72: 111

step-by-step explanation:

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