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 a = 0.05 level of significance? a. For this study, we should use (Select an answer b. The null and alternative hypotheses would be: Ho: ? Select an answer H1: Select an answer v C. The test statistic (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is (? a f. Based on this, we should (Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest that the population mean is not significantly more than 26 at a = 0.05, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is more than 26. O The data suggest that the populaton mean is significantly more than 26 at a = 0.05, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is more than 26. O The data suggest that the sample mean is not significantly more than 26 at a = 0.05, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is more than 27.5. h. Interpret the p-value in the context of the study. OIf the population mean mpg for your car on the highway is 26 and if you take another 55 trips on the highway then there would be a 3.23751601% chance that the sample mean mpg for these 55 trips would be greater than 27.5. There is a 3.23751601% chance of a Type I error.
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 a = 0.05 level of significance? a. For this study, we should use (Select an answer b. The null and alternative hypotheses would be: Ho: ? Select an answer H1: Select an answer v C. The test statistic (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is (? a f. Based on this, we should (Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest that the population mean is not significantly more than 26 at a = 0.05, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is more than 26. O The data suggest that the populaton mean is significantly more than 26 at a = 0.05, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is more than 26. O The data suggest that the sample mean is not significantly more than 26 at a = 0.05, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is more than 27.5. h. Interpret the p-value in the context of the study. OIf the population mean mpg for your car on the highway is 26 and if you take another 55 trips on the highway then there would be a 3.23751601% chance that the sample mean mpg for these 55 trips would be greater than 27.5. There is a 3.23751601% chance of a Type I error.
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd16ddfa-c201-4e3f-90ee-e0e9ce8bf5de%2Fc812b45b-6dbe-4c2b-b94c-6248d62c114f%2F06x4itm_processed.jpeg&w=3840&q=75)
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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