To answer this question, we need to perform a hypothesis test. Here are the steps:

1. State the null hypothesis (Ho) and the alternative hypothesis (Ha). In this case, Ho: μA ≤ μB (the mean mpg of Model A is less than or equal to the mean mpg of Model B) and Ha: μA μB (the mean mpg of Model A is greater than the mean mpg of Model B).

2. Calculate the test statistic. We use the formula for the test statistic in a two-sample t-test:

t = [(mean1 - mean2) - (μ1 - μ2)] / sqrt[(s1^2/n1) + (s2^2/n2)]

where mean1 and mean2 are the sample means, μ1 and μ2 are the population means (which are 0 under the null hypothesis), s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Substituting the given values, we get:

t = [(29.8 - 27.3) - 0] / sqrt[(2.56^2/24) + (1.81^2/28)] = 2.5 / sqrt[0.2733 + 0.1164] = 2.5 / 0.661 = 3.78

3. Determine the critical value for a .05 level of significance. For a one-tailed t-test with df = min(n1, n2) - 1 = min(24, 28) - 1 = 23 degrees of freedom, the critical value is approximately 1.714 (you can find this value in a t-distribution table).

4. Compare the test statistic with the critical value. If the test statistic is greater than the critical value, we reject the null hypothesis. In this case, 3.78 1.714, so we reject Ho.

So, the conclusion is "Reject Ho", which means we have enough evidence at the .05 level of significance to conclude that the miles-per-gallon performance of Model A is greater than the miles-per-gallon performance of Model B.

Question

To answer this question, we need to perform a hypothesis test. Here are the steps:

1. State the null hypothesis (Ho) and the alternative hypothesis (Ha). In this case, Ho: μA ≤ μB (the mean mpg of Model A is less than or equal to the mean mpg of Model B) and Ha: μA > μB (the mean mpg of Model A is greater than the mean mpg of Model B).

2. Calculate the test statistic. We use the formula for the test statistic in a two-sample t-test:

t = [(mean1 - mean2) - (μ1 - μ2)] / sqrt[(s1^2/n1) + (s2^2/n2)]

where mean1 and mean2 are the sample means, μ1 and μ2 are the population means (which are 0 under the null hypothesis), s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Substituting the given values, we get:

t = [(29.8 - 27.3) - 0] / sqrt[(2.56^2/24) + (1.81^2/28)] = 2.5 / sqrt[0.2733 + 0.1164] = 2.5 / 0.661 = 3.78

3. Determine the critical value for a .05 level of significance. For a one-tailed t-test with df = min(n1, n2) - 1 = min(24, 28) - 1 = 23 degrees of freedom, the critical value is approximately 1.714 (you can find this value in a t-distribution table).

4. Compare the test statistic with the critical value. If the test statistic is greater than the critical value, we reject the null hypothesis. In this case, 3.78 > 1.714, so we reject Ho.

So, the conclusion is "Reject Ho", which means we have enough evidence at the .05 level of significance to conclude that the miles-per-gallon performance of Model A is greater than the miles-per-gallon performance of Model B.

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