For multiple sclerosis patients we wish to estimate the mean age at which the disease was first diagnosed. We want a 95% confidence interval that is 10 years wide. If the population variance is 90, how large should our sample be?
To find the sample size needed to estimate the mean age at which multiple sclerosis was first diagnosed with a 95% confidence interval that is 10 years wide, we can use the following formula:
n = (Z^2 * σ^2) / E^2
Where:
n = sample size
Z = Z-score for a 95% confidence interval = 1.96
σ^2 = population variance = 90
E = margin of error = 10
Plugging in the values:
n = (1.96^2 * 90) / 10^2
n = (3.8416 * 90) / 100
n = 345.744 / 100
n ≈ 3.46
Therefore, we would need a sample size of at least 346 patients to estimate the mean age at which multiple sclerosis was first diagnosed with a 95% confidence interval that is 10 years wide.