Question

A sample of 40 observations is selected from a normal population. The sample mean is 31, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level.

H₀: μ ≤ 30

H₁: μ > 30

1. Is this a one- or two-tailed test?

• "One-tailed"—the alternate hypothesis is greater than direction.

• "Two-tailed"—the alternate hypothesis is different from direction.

2. What is the decision rule? (Round your answer to 3 decimal places.)

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

4. What is your decision regarding H₀?

• Do not reject

• Reject

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

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

Answer 1

Solution :

= 30

=31

=3

n = 40

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :    < 30

H_a : >30

Test statistic = z

= ( - ) / / n

= 31(-30) / 3 / 40

= 2.11

Test statistic = z = 2.11

The critical value = 1.645

Test statistic > The critical value

P(z > 2.11 ) = 1 - P(z < 2.11 ) =  0.9826

P-value =0.0174

= 0.05  

P-value <

0.0174 <0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that