You are the operations manager for an airline and you are considering a higher f

Question

You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you? survey? Assume that you want to be 90?% confident that the sample percentage is within 1.5 percentage points of the true population percentage. Complete parts? (a) and? (b) below. a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. nequals nothing ?(Round up to the nearest? integer.) b. Assume that a prior survey suggests that about 31?% of air passengers prefer an aisle seat. nequals nothing ?(Round up to the nearest? integer.)

Explanation / Answer

a) At 90% confidence interval the critical value is z0.05 = 1.645

Margin of error = 1.5

or, z0.05 * sqrt(p(1 - p)/n) = 1.5

or, 1.645 * sqrt(0.5 * 0.5/n) = 1.5

or, sqrt(n) = 1.645 * sqrt(0.5 * 0.5)/1.5

or, n = (1.645 * sqrt(0.5 * 0.5)/1.5)^2

or, n = 1

b) Margin of error = 1.5

or, z0.05 * sqrt(p(1 - p)/n) = 1.5

or, 1.645 * sqrt(0.31 * 0.69/n) = 1.5

or, sqrt(n) = 1.645 * sqrt(0.31 * 0.69)/1.5

or, n = (1.645 * sqrt(0.31 * 0.69)/1.5)^2

or, n = 1

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