Question

A sample of 30 observations is selected from a normal population. The sample mean is 22, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.01 significance level. H0: μ ≤ 20 H1: μ > 20

What is the value of the test statistic? (Round your answer to 2 decimal places.)

What is the p-value? (Round your answer to 4 decimal places.)

Interpret the p-value? (Round your final answer to 2 decimal places.) (% chance of finding a z-value this large by "sampling error" when H0 is true)

Answer 1

Solution :

= 20

= 22

= 4

n = 30

This is the right tailed test .

The null and alternative hypothesis is

H0 :   20

Ha : > 20

Test statistic = z

= ( - ) / / n

= ( 22- 20) /4 / 30

= 2.74

p(Z > 2.74) = 1-P (Z < 2.74) =0.0031

P-value = 0.0031

= 0.01

0.0031< 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that