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?

Answer 1

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.