Question

A random sample of size 100 is selected from a population. The sample mean is 6. The population standard deviation is 2. Use the p-value method and the traditional method to test the claim that the population means is not equal to 5.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 5

H_a :    5

Test statistic = z

= ( - ) / / n

= (6 - 5) / 2 / 100

= 5

P(z > 5) = 1 - P(z < 5) = 0

P-value = 0

= 0.05

P-value <

Reject the null hypothesis .