Question

A sample of 42 observations is selected from one population with a population standard deviation of 4.5. The sample mean is 100.5. A sample of 56 observations is selected from a second population with a population standard deviation of 3.8. The sample mean is 98.5. Conduct the following test of hypothesis using the 0.10 significance level.

H₀ : μ₁ = μ₂

H₁ : μ₁ ≠ μ₂

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

• One-tailed test

• Two-tailed test

2. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

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

4. What is your decision regarding H₀?

• Reject H₀

• Do not reject H₀

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

Answer 1

This is two tailed test, for α = 0.1

Critical value of z are -1.64 and 1.64.
Hence reject H0 if z < -1.64 or z > 1.64

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(20.25/42 + 14.44/56)
sp = 0.8602

Test statistic,
z = (x1bar - x2bar)/sp
z = (100.5 - 98.5)/0.8602
z = 2.33

fail to reject null hypothesis.

P-value Approach
P-value = 0.0198