The average mpg usage for a 2004 Ford Expedition 2WD for a sample of 10 tanks of gas was 17.0with a standard deviation of 0.8. For a Ford Explorer 2WD, the average mpg usage for a sample of 10 tanks of gas was 18.5 with a standard deviation of 1.0. (a) Assuming equal variances, at á = .01, is the true mean mpg lower for the Ford Expedition? (b) Calculate the p-value using Excel.

To determine if the true mean mpg is lower for the Ford Expedition compared to the Ford Explorer, we can conduct a two-sample t-test.

(a) For this test, we will use a significance level (α) of 0.01. To perform a two-sample t-test assuming equal variances, we need to calculate the test statistic and compare it to the critical value.

The test statistic for a two-sample t-test assuming equal variances is given by:

t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))

Where:
x1 and x2 are the sample means,
s1 and s2 are the sample standard deviations,
n1 and n2 are the sample sizes.

In this case:
x1 = 17.0 (average mpg for Ford Expedition)
x2 = 18.5 (average mpg for Ford Explorer)
s1 = 0.8 (standard deviation for Ford Expedition)
s2 = 1.0 (standard deviation for Ford Explorer)
n1 = n2 = 10 (both samples have 10 tanks of gas)

Substituting these values into the formula, we get:

t = (17.0 - 18.5) / sqrt((0.8^2 / 10) + (1.0^2 / 10))

Calculating this expression gives us t = -2.0655

To determine the critical value, we need to find the degrees of freedom. For a two-sample t-test with equal variances, the degrees of freedom are calculated using the following formula:

df = n1 + n2 - 2
= 10 + 10 - 2
= 18

Using a t-table or statistical software, we can find the critical t-value for a significance level of 0.01 and 18 degrees of freedom. The critical value is approximately -2.878.

Since the calculated test statistic (-2.0655) is not less than the critical value (-2.878), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the true mean mpg of the Ford Expedition is lower than that of the Ford Explorer.

(b) To calculate the p-value using Excel, you can use the TTEST function. Follow these steps:

1. Open a new Excel spreadsheet and organize your data. In a column, list the 10 mpg measurements for the Ford Expedition and in another column, list the 10 mpg measurements for the Ford Explorer.
2. In an empty cell, type "=TTEST(range1, range2, tails, type)".
3. Replace "range1" with the cell range for the Ford Expedition mpg measurements and "range2" with the cell range for the Ford Explorer mpg measurements. For example, if your data is in cells A2:A11 and B2:B11, the formula would be "=TTEST(A2:A11, B2:B11, 1, 2)".
4. Replace "tails" with the number of tails you expect. Since we are testing if the true mean of the Ford Expedition is lower than that of the Ford Explorer, we use 1-tail.
5. Replace "type" with the type of t-test you want to perform. In this case, since we are assuming equal variances, we use 2 (two-sample equal variances).
6. Press Enter to calculate the p-value.

The Excel TTEST function will return the p-value. If the calculated p-value is less than the significance level (0.01), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.