Question

A sample of 39 observations is selected from a normal population. The sample mean is 43, and the population standard deviation is 6. Conduct the following test of hypothesis using the 0.02 significance level.

H₀: μ = 45

H₁: μ ≠ 45

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

• One-tailed test

• Two-tailed test

2. What is the decision rule?

• Reject H₀ if −2.326 < z < 2.326

• Reject H₀ if z < −2.326 or z > 2.326

3. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

4. What is your decision regarding H₀?

• Reject H₀

• Fail to reject H₀

1. e-1. What is the p-value? (Round your z value to 2 decimal places and final answer to 4 decimal places.)

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

Answer 1

a) Two-tailed test

b) Reject H0 if −2.326 < z < 2.326

c)

n =39

Null and alternative hypothesis is

H0 : u =45

H1 : u ≠45

Level of significance = 0.02

Here population standard deviation is known so we use z-test statistic.

Test statistic is

Degrees of freedom = n - 1 = 39-1=38

critical value = 2.326

critical value > Test statistic ,Failed to Reject H0

d) Fail to reject H₀

e-1)

P-value = 0.0374 ( using z table)

e-2)

Interpretation : 3.74 % we are taking risk to rejecting null hypothesis.