Question

Given the following values: μ = 6.0, M = 7.6, n = 36, σ = 6, conduct a one-sample z test at a 0.05 level of significance. For a one-tailed test, upper-tail critical, what is the decision?

a. to reject the null hypothesis
b. to retain the null hypothesis
c. There is not enough information since the sample size is not given.

Answer 1

b) We accept H₀

Explanation:

We assume Normal Distribution

Population mean μ₀ = 6

Sample size = n n = 36 n > 30

Sample mean = 7.6

Sample standard deviation s = 6

1.- Hypothesis test:

We are ask for a one-tail test upper-tail critical then

H₀ null hipothesis μ₀ = 6

Hₐ Alternative hypothesis μ₀ > 6

2.-

Level of significance α = 0.05 from z table we find value of z(c)

z(c) = 1.64

3.-Compute z(s)

z(s) = ( μ - μ₀ ) / s/√n ⇒ z(s) = ( 7.6 - 6 ) / 6/√36

z(s) = 1.6

4.-Compare

z(s) and z(c)

z(s) = 1.6 and z(c) = 1.64 then

z(s) < z(c)

z(s) is inside the acceptance region. We accept H₀