Question

A sample of 31 observations is selected from a normal population. The sample mean is 11, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level.

H₀: μ ≤ 10

H₁: μ > 10

1. e-1. What is the p-value? (Round your answer to 4 decimal places.)

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

Answer 1

Solution :

= 10

=11

=3

n = 31

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   < 10

H_a : > 10

Test statistic = z

= ( - ) / / n

= (11-10) / 3 / 32

= 1.85

Test statistic = z = 1.85

P(z > 1.85) = 1 - P(z < 1.85 ) = 0.9678

P-value =0.0322

= 0.05  

P-value <

0.0322 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that