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 9595% confident that the sample percentage is within 2.52.5 percentage points of the true population percentage. complete parts (a) and (b) below.

Recall that margin of error is given by:



Given that you want to be 95% confident that the sample percentage is within 2.5 percentage points of the true population percentage.

This means that and M = 2.5% = 0.025.

Part A:

When nothing is known about the percentage of persengers who prefer aisle seat, we make use of p = 50% = 0.5.

Thus,



Therefore, 1,537 randomly selected air passengers must be surveyed to be 95% confident that the sample percentage is within 2.5 percentage points of the true population percentage.

Part B:

Given that recent surveys surgest that about 38% of all air passengers prefer an aisle seat, thus p = 38% = 0.38

Thus,



Therefore, 1,449 randomly selected air passengers must be surveyed to be 95% confident that the sample percentage is within 2.5 percentage points of the true population percentage.

1,537  randomly selected air passengers must be surveyed to be 95 percent confident within 2.5 percentage points of the sample percentage by using p=50 percent.1,449  randomly selected air passengers must be surveyed to be 95 percent confident within 2.5 percentage points of the sample percentage by using p=38 percent.

Step by Step Explanation:

You want 95% confidence within 2.5% points of the actual population.

The margin of error can be formulated as given below:

Part-(A)

Using p=50%

Substitute the values in the above formula and solve for the n.

Thus,

n=1537.

Part-(B)

Substitute the values in the above formula and solve for the n.

Thus,

n=1449.

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