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To calculate the test statistic for the provided data, we will conduct a paired \( t \)-test since each car provides paired observations for both regular and premium gas mileage. Here’s the step-by-step process:

### 1. Record the Data
From the table:
- **Regular gas (sample 1)**: \( 16, 20, 21, 23, 22, 27, 25, 27, 28, 22 \)
- **Premium gas (sample 2)**: \( 19, 22, 24, 25, 25, 26, 26, 28, 32, 24 \)

### 2. Calculate the Differences (\( d \)) Between the Two Samples
For each car:
\[
d = \text{Premium MPG} - \text{Regular MPG}
\]
The differences are:
\[
d = 3, 2, 3, 2, 3, -1, 1, 1, 4, 2
\]

### 3. Compute the Mean and Standard Deviation of Differences (\( \bar{d} \) and \( s_d \))
- Mean of the differences (\( \bar{d} \)):
\[
\bar{d} = \frac{\sum d}{n} = \frac{(3 + 2 + 3 + 2 + 3 - 1 + 1 + 1 + 4 + 2)}{10} = \frac{20}{10} = 2
\]

- Standard deviation of the differences (\( s_d \)):
\[
s_d = \sqrt{\frac{\sum (d - \bar{d})^2}{n - 1}}
\]
First, calculate \( (d - \bar{d})^2 \):
\[
(3 - 2)^2 = 1, \; (2 - 2)^2 = 0, \; (3 - 2)^2 = 1, \; (2 - 2)^2 = 0, \; (3 - 2)^2 = 1, \; (-1 - 2)^2 = 9, \; (1 - 2)^2 = 1, \; (1 - 2)^2 = 1, \; (4 - 2)^2 = 4, \; (2 - 2)^2 = 0
\]

Sum of squared deviations:
\[
\sum (d - \bar{d})^2 = 1 + 0 + 1 + 0 + 1 + 9 + 1 + 1 + 4 + 0 = 18
\]

Standard deviation:
\[
s_d = \sqrt{\frac{18}{10 - 1}} = \sqrt{2} \approx 1.414
\]

### 4. Compute the Test Statistic (\( t \)-value)
The test statistic for a paired \( t \)-test is:
\[
t = \frac{\bar{d}}{s_d / \sqrt{n}}
\]
Substitute the values:
\[
t = \frac{2}{1.414 / \sqrt{10}} = \frac{2}{1.414 / 3.162} = \frac{2}{0.447} \approx 4.48
\]

### Final Answer
The test statistic is approximately:
\[
t \approx 4.48
\]

Would you like further assistance, such as finding the critical \( t \)-value or interpreting the results? 

---

### 5 Related Questions:
1. How is the critical \( t \)-value calculated for a 90% confidence level?
2. Can you determine if the result is statistically significant?
3. What assumptions are made when conducting a paired \( t \)-test?
4. How does sample size affect the test statistic?
5. What is the importance of using paired differences in this scenario?

### Tip:
Always check for outliers in paired data, as they can disproportionately influence the test statistic and conclusions.

Explore the statistical calculation of the t-test statistic to compare the efficiency rates of regular and premium gas using paired data from 10 cars. Includes detailed steps for hypothesis testing, calculating mean differences, and using the t-distribution.

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