Question

A sample of 35 observations is selected from a normal population. The sample mean is 20, and the population standard deviation is 2. Conduct the following test of hypothesis using the 0.05 significance level.

H₀: μ ≤ 19

H₁: μ > 19

Interpret the p-value? (Round your final answer to 2 decimal places.)

Answer 1

This is the right tail test .

The null and alternative hypothesis is ,

H₀ :   ≤ 19

H_a :    > 19

Test statistic = z

= ( - ) / / n

= (20-19) / 2 / 35

= 2.96

P(z >2.96 ) = 1 - P(z < 2.96 ) = 1-0.9985=0.0015

P-value = 0.0015

= 0.05  

P-value <

Reject the null hypothesis