Question

A sample of 45 observations is selected from a normal population. The sample mean is 49, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.10 significance level.

H₀: μ = 51

H₁: μ ≠ 51

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

• One-tailed test

• Two-tailed test

2. What is the decision rule?

• Reject H₀ if −1.645 < z < 1.645

• Reject H₀ if z < −1.645 or z > 1.645

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?

• Fail to reject H₀

• 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

Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are -1.645 and 1.645.
Hence reject H0 if z < -1.645 or z > 1.645

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (49 - 50)/(5/sqrt(45))
z = -1.34

Fail to reject H0

P-value Approach
P-value = 0.1802

As P-value >= 0.1, fail to reject null hypothesis.