You are designing a study to determine whether music has an effect on learning. Previous research indicates that the standard deviation to learn a task is 3.4 minutes. How many subjects would you need to ensure with 90% confidence that the estimate is within 1 minute of the true mean time required?
To determine the sample size needed for your study, you can use the formula for sample size calculation in estimating the mean of a population:
n = (Z * σ / E)^2
Where:
n = sample size
Z = z-score corresponding to the desired confidence level (in this case, 90% confidence)
σ = standard deviation of the population
E = desired margin of error (in this case, 1 minute)
First, we need to find the z-score for a 90% confidence level. We can use a standard normal distribution table or a statistical software to find that the z-score corresponding to a 90% confidence level is approximately 1.645.
Next, we substitute the known values into the formula:
n = (1.645 * 3.4 / 1)^2
n = (5.5813 / 1)^2
n = 31.1349^2
n ≈ 970.29
Since you cannot have a fractional number of subjects, you would need a minimum of 971 subjects to ensure with 90% confidence that the estimate is within 1 minute of the true mean time required.