Question

Suppose that for some population, intelligence scores are distributed normally with σ = 15 and with μ unknown. To
construct a confidence interval for μ, based on the mean of a sample, how large a sample of scores is necessary so
that the probability is A: 0.9 that μ will be:

a) Within 12 points of the sample mean?

b) Within 6 points of the sample mean?

c) Within 3 points of the sample mean?

d) Within 0.5 point of the sample mean?

Answer 1

a) At 90% confidence level, the critical value is z_0.05 = 1.645

Margin of error = 12

or, z_0.05 * = 12

ulo

or, 1.645 * 15/$\sqrt n$ = 12

or, n = (1.645 * 15/12)^2

or, n = 5

b) Margin of error = 6

or, z_0.05 * = 6

ulo

or, 1.645 * 15/$\sqrt n$ = 6

or, n = (1.645 * 15/6)^2

or, n = 17

c) Margin of error = 3

or, z_0.05 * = 3

ulo

or, 1.645 * 15/$\sqrt n$ = 3

or, n = (1.645 * 15/3)^2

or, n = 68

d) Margin of error = 0.5

or, z_0.05 * = 0.5

ulo

or, 1.645 * 15/$\sqrt n$ = 0.5

or, n = (1.645 * 15/0.5)^2

or, n = 2436