MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Hypothesis Testing for Mean MPG

The manufacturer claims that your new car gets 26 mpg on the highway. You suspect that the mpg is more for your car. The 55 trips on the highway that you took averaged 27.5 mpg and the standard deviation for these 55 trips was 5.9 mpg. What can be concluded at the \( \alpha = 0.05 \) level of significance?

#### Steps to Perform Hypothesis Testing

1. **Selecting the Type of Test:**
   - For this study, we use the [Select an answer] test.

2. **Formulating Hypotheses:**
   - The null and alternative hypotheses are:
     \[
     H_0: \text{mean} \, \mu = 26 \text{ mpg}
     \]
     \[
     H_1: \text{mean} \, \mu > 26 \text{ mpg}
     \]

3. **Calculating the Test Statistic:**
   - The test statistic \( t \) is calculated as:
     \[
     t = \frac{\bar{x} - \mu}{s / \sqrt{n}} = \frac{27.5 - 26}{5.9 / \sqrt{55}} = \left[ \text{Please show your answer to 3 decimal places} \right]
     \]

4. **Determining the p-value:**
   - The p-value is \( [ \text{Please show your answer to 4 decimal places} ] \).

5. **Comparing p-value to Alpha:**
   - If the p-value is less than \( \alpha \):
     \[
     \text{Reject } H_0
     \]
   - If the p-value is greater than \( \alpha \):
     \[
     \text{Fail to reject } H_0
     \]

6. **Conclusion:**
   - Based on this, we [Select an answer] the null hypothesis.

7. **Final Conclusion:**
   - Depending on the comparison, the final conclusion can be:
     \[
     \begin{cases}
       & \text{The data suggest that the population mean is not significantly more than 26 at } \alpha = 0.05, \\
       & \text{so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is more than
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Transcribed Image Text:### Hypothesis Testing for Mean MPG The manufacturer claims that your new car gets 26 mpg on the highway. You suspect that the mpg is more for your car. The 55 trips on the highway that you took averaged 27.5 mpg and the standard deviation for these 55 trips was 5.9 mpg. What can be concluded at the \( \alpha = 0.05 \) level of significance? #### Steps to Perform Hypothesis Testing 1. **Selecting the Type of Test:** - For this study, we use the [Select an answer] test. 2. **Formulating Hypotheses:** - The null and alternative hypotheses are: \[ H_0: \text{mean} \, \mu = 26 \text{ mpg} \] \[ H_1: \text{mean} \, \mu > 26 \text{ mpg} \] 3. **Calculating the Test Statistic:** - The test statistic \( t \) is calculated as: \[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} = \frac{27.5 - 26}{5.9 / \sqrt{55}} = \left[ \text{Please show your answer to 3 decimal places} \right] \] 4. **Determining the p-value:** - The p-value is \( [ \text{Please show your answer to 4 decimal places} ] \). 5. **Comparing p-value to Alpha:** - If the p-value is less than \( \alpha \): \[ \text{Reject } H_0 \] - If the p-value is greater than \( \alpha \): \[ \text{Fail to reject } H_0 \] 6. **Conclusion:** - Based on this, we [Select an answer] the null hypothesis. 7. **Final Conclusion:** - Depending on the comparison, the final conclusion can be: \[ \begin{cases} & \text{The data suggest that the population mean is not significantly more than 26 at } \alpha = 0.05, \\ & \text{so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is more than
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