SOLUTION: Toyota provides an opinion of a sunroof and side air bag package for its corolla model. This package cost $1400 (1159 invoice price). Assume that prior to offering this option, Toy

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Question 1058522: Toyota provides an opinion of a sunroof and side air bag package for its corolla model. This package cost $1400 (1159 invoice price). Assume that prior to offering this option, Toyota wants to determine the percentage of corolla buyers who would pay $1400 extra for the sunroof and side air bag. How many corolla buyers must be surveyed if we want to be 92% confident that the sample percentage is within four percentage points of the true percentage for all corolla buyers?
Answer by solve_for_x(190) About Me  (Show Source):
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The required sample size is:

n+=+%28p%29%281+-+p%29%28z%2FE%29%5E2

For a 92% confidence level, use z = 1.751.

The value of E is 0.04.

Since we don't know anything about the population percentage that will
pay extra for the options, use p = 0.5 as a conservative estimate.

The required sample size is then:

n+=+%280.5%29%281+-+0.5%29%281.751%2F.04%29%5E2

n = 479.06

Since this is a minimum value, and the sample size must be a whole number,
this result must be rounded up to the next whole number.

Solution: Sample size = 480