A researcher wishes to estimate, with 95 95% confidence, the population proporti

Question

A researcher wishes to estimate, with 95 95% confidence, the population proportion of adults who say chocolate is their favorite ice cream flavor. Her estimate must be accurate within 1 1% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 20 20% of the respondents said their favorite flavor of ice cream is chocolate. (c) Compare the results from parts (a) and (b).

Explanation / Answer

A) At 95% confidence interval the critical value is z* = 1.96

Margin of error = 0.01

Or, z* * sqrt(P(1 - p)/n) = 0.01

Or, 1.96 * Sqrt((0.5 * 0.5)/n) = 0.01

Or, n = (1.96 * Sqrt(0.5 * 0.5)/0.01)^2

Or, n = 9604

B) Margin of error = 0.01

Or, z* * sqrt(p(1 - p)/n) = 0.01

Or, 1.96 * Sqrt(0.2 * 0.8/n) = 0.01

Or, n = (1.96 * Sqrt(0.2 * 0.8)/0.01)^2

Or, n = 6147

C) The sample size for no preliminary estimate is larger.

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