Consider the following competing hypotheses and relevant summary statistics:
H₀: σ₁²/σ₂² = 1
Hₐ: σ₁²/σ₂² ≠ 1
Sample 1: x̄₁ = 45.3, s₁² = 17.6, and n₁ = 6
Sample 2: x̄₂ = 48.1, s₂² = 11.4, and n₂ = 4
Assume that the two populations are normally distributed. (You may find it useful to reference the appropriate table: chi-square table or F table)
a. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
b. Find the p-value.
0.01 ≤ p-value < 0.025
p-value < 0.01
p-value > 0.10
0.05 ≤ p-value < 0.10
0.025 ≤ p-value < 0.05
c. Do you reject the null hypothesis at the 10% significance level?
Yes, since the p-value is less than the significance level.
No, since the p-value is more than the significance level.
d. Interpret the results at α = 0.10.
We conclude that the population variances differ.
We cannot conclude that the population variances differ.
We conclude that population variance 1 is greater than population variance 2.
We cannot conclude that population variance 1 is greater than population variance 2.