Question

A random sample of ? measurements was selected from a population with standard deviation σ=11.7 and unknown mean μ. Calculate a 90 % confidence interval for μ for each of the following situations:

(a) ?=40, ?=72.1
≤. μ ≤

(b)  ?=60, ?=72.1
μ ≤

(c)  ?=85, ?=72.1
≤. μ. ≤

Answer 1

a)

90% confidence interval for is

- Z * / sqrt(n) < < - Z * / sqrt(n)

72.1 - 1.645 * 11.7 / sqrt(40) < < 72.1 + 1.645 * 11.7 / sqrt(40)

69.06 < < 75.14

90% CI is ( 69.06 , 75.14 )

b)

90% confidence interval for is

- Z * / sqrt(n) < < - Z * / sqrt(n)

72.1 - 1.645 * 11.7 / sqrt(60) < < 72.1 + 1.645 * 11.7 / sqrt(60)

69.62 < < 74.58

90% CI is ( 69.62 , 74.58)

b)

90% confidence interval for is

- Z * / sqrt(n) < < - Z * / sqrt(n)

72.1 - 1.645 * 11.7 / sqrt(85) < < 72.1 + 1.645 * 11.7 / sqrt(85)

70.01 < < 74.19

90% CI is ( 70.01 , 74.19 )