In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the
Standard deviation is 4.5 hours. How large a sample must be selected?
A)20
B)4
C)5
D)19

Question

Quizplus · Accepted Answer

To determine the sample size needed for a specific margin of error (E) with a given confidence level and standard deviation (σ), we use the formula for the sample size in estimating a mean, which is $n = \left(\frac{Z\sigma}{E}\right)^2$. For a 95% confidence level, the Z-value (Z-score) is approximately 1.96. Given that the standard deviation (σ) is 4.5 hours and the desired margin of error (E) is 2 hours, we substitute these values into the formula: $n = \left(\frac{1.96 \times 4.5}{2}\right)^2$, which calculates to approximately 19.36. Since the sample size must be a whole number, we round up to the nearest whole number, which is 20.

In Order to Efficiently Bid on a Contract, a Contractor