The manager of Alco wants to establish the proportion of time that the stock clerks spend making price changes on previously marked merchandise. The manager wants a 98% confidence that the resulting estimate will be within 5% of the true value. What sample size should be used?
To determine the sample size needed to estimate the proportion of time stock clerks spend making price changes on previously marked merchandise with a specified confidence level and margin of error, we can use the formula for sample size calculation for proportions.
The formula for sample size calculation for proportions is:
n = (Z² * P * (1 - P)) / E²
Where:
- n is the desired sample size
- Z is the Z-value corresponding to the desired confidence level (98% confidence level corresponds to Z = 2.33)
- P is the estimated proportion of the population parameter
- E is the desired margin of error (5% of the true value)
In this case, the manager wants a 98% confidence level, which corresponds to Z = 2.33. The manager also wants the estimate to be within 5% of the true value, so the margin of error (E) is 0.05.
However, the estimated proportion of the population parameter (P) is not given in the question. Without that information, it is not possible to calculate the exact sample size. The proportion could be estimated based on previous data or previous studies, but without that information, we cannot provide an exact sample size.
To calculate the sample size, the manager needs to provide an estimate for the proportion (P) based on either historical data or a reasonable guess.