Question

A researcher who wants to test the hypothesis that the population mean of a variable is 85, takes a sample of 50 people and obtains a sample mean of 81. A hypothesis test finds that the sample mean is not significantly different from the hypothesized population mean at 5% level of significance. What could be a 95% confidence interval for the population mean?

Answer 1

CI = ( 28,28 - 1,96*σ ; 28,28 + 1,96*σ )

Explanation:

Population mean μ₀ = 85

Sample size n = 50

Sample mean μ = 81

Significance Level α = 5 % α = 0,05

From Hypothesis Test

Null Hypothesis H₀ μ = μ₀

Alternative Hypothesis Hₐ μ ≠ μ₀

After a two taio-test was found no significative difference about the mean

Then α/2 = 0,05/2 α/2 = 0,025

CI = 95 % CI = 0,95

From z-table

z(c) = (±) 1,96

CI = ( μ - μ₀ ) ± z(c) * σ/√50

CI = ( 85 - 81 )*√50 ± 1,96 *σ

CI = 4*7,07 ± 1,96*σ

CI = ( 4*7,07 - 1,96*σ ; 4*7,07 + 1,96*σ )

CI = ( 28,28 - 1,96*σ ; 28,28 + 1,96*σ )