The average mpg usage for a 2009 Toyota Prius for a sample of 24 tanks of gas wa

Question

The average mpg usage for a 2009 Toyota Prius for a sample of 24 tanks of gas was 45.8 with a standard deviation of 1.6. For a 2009 Honda Insight, the average mpg usage for a sample of 24 tanks of gas was 43.7 with a standard deviation of 2.6. Assuming equal variances, at a = 0.01, is the true mean mpg lower for the Honda Insight? (a-1) Choose the appropriate hypotheses. H_0: mu_toy - mu_hon lessthanorequalto 0 vs. H_1: mu_toy - mu_hon > 0. Reject H_0 if t_calc > 2.410 H_0: mu_toy - mu_hon lessthanorequalto 0 vs. H_1: mu_toy - mu_hon > 0. Reject H_0 if t_calc

Explanation / Answer

The statistical software output for the given problem is:

Two sample T hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 > 0
(with pooled variances)

Hypothesis test results:

a - 1: For 46 degrees of freedom and 0.01 level of significance,

Critical t - value = 2.41

So,

Option 1 is correct.

a - 2: tcalc = 3.3699

a - 3: Reject the null hypothesis since calculated value of t lies in the rejection region.

Option 2 is correct.

a - 4: Yes since we rejected the null hypothesis.

Option 1 is correct.

b) p - value = 0.0008

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 2.1 0.62316397 46 3.3698996 0.0008

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