Module 3 Quiz

Question 2

Brand A gasoline was used in 16 similar automobiles under identical conditions. The corresponding sample of 16 values (miles per gallon) had mean 19.6 and standard deviation 0.4. Under the same conditions, high-power brand B gasoline gave a sample of 16 values with mean 20.2 and standard deviation 0.6. Is the mileage of B significantly better than that of A? Assume normality. Test the hypothesis using both P-value and fixed significance level with α=0.05 approaches (if possible).

Given

A: n = 16, x¯ = 19.6, σ = 0.4
B: n = 16, x¯ = 20.2, σ = 0.6
α = 0.05

Seven-Step Hypothesis-Testing Procedure

1. Parameter of interest: The parameter of interest is the mileage mean of the two brands of gasolines, A and B, μ1 and μ2 respectively.

2. Null hypothesis: H0: μ1 = μ2

3. Alternative Hypothesis: H1: μ1 < μ2

4. Test Statistic:

figure 1.

5. Reject H0 if: P-value is less than α = 0.05.

6. Computations:

figure 2.

7. Conclusions: Since the P-value is 0.00043 which is less than α = 0.05, we reject the null hypothesis. Therefore, it is evident that the mileage of brand B is significantly better than that of brand A.