A. What is the parameter of interest, and what is the point estimate? Be sure to include notation for both the parameter and the point estimate. B. Check the conditions for doing inference on the parameter of interest.

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A. What is the parameter of interest, and what is the point estimate? Be sure to include notation for both the parameter and the point estimate.

B. Check the conditions for doing inference on the parameter of interest.

Each year, the US Environmental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. We took random samples of cars with manual and automatic transmissions manufactured in 2021 and recorded the on-highway fuel efficiency (in miles per gallon) for each car. We want to investigate the difference between the mean highway fuel efficiency (mpg) for cars with manual transmissions and the mean highway fuel efficiency (mpg) for cars with automatic transmissions.

Use the following R output to answer the questions that follow.

**Graph Descriptions:**

1. **Histogram for MPG of Manual Cars:**
   - The histogram displays the frequency distribution of highway mpg for manual cars.
   - Frequency ranges from 0 to 10.
   - MPG values range from 20 to 45.
   - The data appears to be centered around 30, with most values between 25 and 35 mpg.

2. **Histogram for MPG of Automatic Cars:**
   - This histogram shows the frequency distribution of highway mpg for automatic cars.
   - Frequency ranges from 0 to 6.
   - MPG values range from 18 to 30.
   - The data is centered around 23, with a higher concentration of values from 18 to 26 mpg.

**Table of Statistics:**

| HIGHWAY   | Mean  | SD    | n  |
|-----------|-------|-------|----|
| Automatic | 23.68 | 3.902 | 25 |
| Manual    | 30.88 | 5.134 | 25 |

- The table includes the mean (average), standard deviation (SD), and sample size (n) for each transmission type.
- Manual cars have a higher mean mpg (30.88) compared to automatic cars (23.68).
- The standard deviation is larger for manual cars (5.134) compared to automatic cars (3.902), suggesting more variability in fuel efficiency for manual cars.
Transcribed Image Text:Each year, the US Environmental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. We took random samples of cars with manual and automatic transmissions manufactured in 2021 and recorded the on-highway fuel efficiency (in miles per gallon) for each car. We want to investigate the difference between the mean highway fuel efficiency (mpg) for cars with manual transmissions and the mean highway fuel efficiency (mpg) for cars with automatic transmissions. Use the following R output to answer the questions that follow. **Graph Descriptions:** 1. **Histogram for MPG of Manual Cars:** - The histogram displays the frequency distribution of highway mpg for manual cars. - Frequency ranges from 0 to 10. - MPG values range from 20 to 45. - The data appears to be centered around 30, with most values between 25 and 35 mpg. 2. **Histogram for MPG of Automatic Cars:** - This histogram shows the frequency distribution of highway mpg for automatic cars. - Frequency ranges from 0 to 6. - MPG values range from 18 to 30. - The data is centered around 23, with a higher concentration of values from 18 to 26 mpg. **Table of Statistics:** | HIGHWAY | Mean | SD | n | |-----------|-------|-------|----| | Automatic | 23.68 | 3.902 | 25 | | Manual | 30.88 | 5.134 | 25 | - The table includes the mean (average), standard deviation (SD), and sample size (n) for each transmission type. - Manual cars have a higher mean mpg (30.88) compared to automatic cars (23.68). - The standard deviation is larger for manual cars (5.134) compared to automatic cars (3.902), suggesting more variability in fuel efficiency for manual cars.
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