Question

A random sample is obtained from a population with a variance of σ²=200, and the sample mean is computed to be x̅_c=60.

Test if the mean value is μ=40.

Test the claim at the 10% significance (α=.10).

Consider the null hypothesis H₀: μ=40 versus the alternative hypothesis H_1:μ≠40

The distribution of the mean is normal

N = 100.

Answer 1

Solution:

Given ,

²= 200

n = 100

= 60

Use = 0.10

Hypothesis are

H0 : μ=40. vs H_1: μ ≠ 40

The test statistic z is

z =     

=

= 14.14

Now , observe that ,there is   sign in H1. So , the test is two tailed

p value = P(Z > 14.14) + P(Z < -14.14) = 0 + 0 = 0

p value is less than = 0.10

Reject H₀

Sufficient evidence to conclude that the mean is different from 40