Question

Consider a random sample of size 14 from a normal population with expected value μ and variance σ2 . Given x̄ = 43.4 and s2 = 186, a 95% confidence interval for μ is given by

Group of answer choices

(36.3, 50.5)

(33.4, 53.4)

(32.4,54.4)

(34.5,52.3)

(35.5, 51.3)

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 43.4

S = Sqrt(186) = 13.63818

n = 14

df = n – 1 = 13

Confidence level = 95%

Critical t value = 2.1604

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 43.4 ± 2.1604*13.63818/sqrt(14)

Confidence interval = 43.4 ± 7.8745

Lower limit = 43.4 - 7.8745 = 35.5

Upper limit = 43.4 + 7.8745 =51.3

Confidence interval = (35.5, 51.3)

Answer: (35.5, 51.3)