Question 1179924: A car salesman claims that the variance of prices on convertibles is higher than the variance of prices on station wagons. The standard deviation of the list price on 16 convertibles is $6800 and the standard deviation on 24 station wagons is $3900. What should the test value be?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the test value for this hypothesis test:
**1. State the Hypotheses:**
* **Null Hypothesis (H0):** The variance of convertible prices is equal to the variance of station wagon prices. (σ₁² = σ₂²)
* **Alternative Hypothesis (H1):** The variance of convertible prices is greater than the variance of station wagon prices. (σ₁² > σ₂²) This is a right-tailed test.
**2. Identify Given Information:**
* Sample standard deviation of convertibles (s₁) = $6800
* Sample size of convertibles (n₁) = 16
* Sample standard deviation of station wagons (s₂) = $3900
* Sample size of station wagons (n₂) = 24
**3. Calculate the Test Statistic (F-statistic):**
The test statistic for comparing two variances is the F-statistic:
F = s₁² / s₂²
Where:
* s₁² is the sample variance of the first group (convertibles).
* s₂² is the sample variance of the second group (station wagons).
First, calculate the variances:
* s₁² = (6800)² = 46,240,000
* s₂² = (3900)² = 15,210,000
Now, calculate the F-statistic:
F = 46,240,000 / 15,210,000
F ≈ 3.04
**Answer:**
The test value (F-statistic) should be approximately 3.04.
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