The proportion of public accountants who have changed companies within the last

Question

The proportion of public accountants who have changed companies within the last three years is to be estimated within 3%. The 95% level of confidence is to be used. A study conducted several years ago revealed that the percent of public accountants changing companies within three years was 23. (Use z Distribution Table.) (Round the z-values to 2 decimal places. Round up your answers to the next whole number.)

How many public accountants should be contacted if no previous estimates of the population proportion are available?

The proportion of public accountants who have changed companies within the last three years is to be estimated within 3%. The 95% level of confidence is to be used. A study conducted several years ago revealed that the percent of public accountants changing companies within three years was 23. (Use z Distribution Table.) (Round the z-values to 2 decimal places. Round up your answers to the next whole number.)

Explanation / Answer

a) At 95% confidence interval the critical value is z0.025 = 1.96

Margin of error = 0.03

or, z0.025 * sqrt(p(1 - p)/n) = 0.03

or, 1.96 * sqrt(0.23 * (1 - 0.23)/n) = 0.03

or, n = (1.96 * sqrt(0.23 * 0.77)/0.03)^2

or, n = 756

b) Margin of error = 0.03

or, z0.025 * sqrt(p(1 - p)/n) = 0.03

or, 1.96 * sqrt(0.5 * 0.5/n) = 0.03

or, n = (1.96 * sqrt(0.5 * 0.5)/0.03)^2

or, n = 1068

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