The manufacturer claims that your new car gets 20 mpg on the highway. You suspect that the mpg is a different number for your car. The 42 trips on the highway that you took averaged 28.1 mpg and the tandard deviation for these 42 trips was 6.5 mpg. What can be concluded at the x = 0.10 level of ignificance? 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 c. The test statistic d. The p-value= e. The p-value is a f. Based on this, we should [Select an answer the null hypothesis. g. Thus, the final conclusion is that ... = (please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.) O The data suggest that the sample mean is not significantly different from 26 at x = 0.10, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is different from 28.1. O The data suggest that the populaton mean is significantly different from 26 at a = 0.10, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is different from 26. O The data suggest that the population mean is not significantly different from 26 at x = 0.10, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is different from 26. h. Interpret the p-value in the context of the study. O There is a 4.25056656% chance that the population mean mpg for your car on the highway is not equal to 26. O If the population mean mpg for your car on the highway is 26 and if you take another 42 trips on the highway, then there would be a 4.25056656% chance that the sample mean for these 42 highway trips would either be less than 24 or greater than 28.1. O There is a 4.25056656% chance of a Type I error. O If the population mean mpg for your car on the highway is 26 and if you take another 42 trips on the highway then there would be a 4.25056656% chance that the population mean would either be less than 24 or greater than 28.1. i. Interpret the level of significance in the context of the study. O If the population mean mpg for your car on the highway is 26 and if you take another 42 trips on the highway, then there would be a 10% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is different from 26. O If the population population mean mpg for your car on the highway is different from 26 and if you take another 42 trips on the highway, then there would be a 10% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is equal to 26. O There is a 10% chance that you own an electric powered car, so none of this matters to you anyway. O There is a 10% chance that the population mean mpg for your car on the highway is different

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
100%

Need help in part D please 0.0582 incorrect

**Hypothesis Testing for Car Mileage**

The manufacturer claims that your new car gets 26 miles per gallon (mpg) on the highway. You suspect that the mpg is different. After 42 trips, you've averaged 28.1 mpg, with a standard deviation of 6.5 mpg. We conduct a hypothesis test at the α = 0.10 level of significance.

**a. For this study, we should use:**
- Select an answer: >, <, ≠

**b. The null and alternative hypotheses would be:**
- \( H_0 \): μ = 26
- \( H_1 \): μ ≠ 26

**c. The test statistic \( z \) is:**
- [Your answer here, rounded to 3 decimal places]

**d. The p-value is:**
- [Your answer here, rounded to 4 decimal places]

**e. The p-value is:**
- ≤ α
- > α

**f. Based on this, we should:**
- Select an answer about the null hypothesis:
  - Reject
  - Fail to reject

**g. Thus, the final conclusion is:**
- The data suggest that the sample mean is not significantly different from 26 at α = 0.10, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is different from 28.1.
- The data suggest that the population mean is significantly different from 26 at α = 0.10, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is different from 26.
- The data suggest that the population mean is not significantly different from 26 at α = 0.10, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is different from 26.

**h. Interpret the p-value in the context of the study.**
- There is a 4.25056656% chance that the population mean mpg for your car on the highway is not equal to 26.
- If the population mean mpg for your car on the highway is 26 and if you take another 42 trips on the highway, then there would be a 4.25056666% chance that the sample mean for these 42 highway trips would either be less than 24 or greater than 28.1.
Transcribed Image Text:**Hypothesis Testing for Car Mileage** The manufacturer claims that your new car gets 26 miles per gallon (mpg) on the highway. You suspect that the mpg is different. After 42 trips, you've averaged 28.1 mpg, with a standard deviation of 6.5 mpg. We conduct a hypothesis test at the α = 0.10 level of significance. **a. For this study, we should use:** - Select an answer: >, <, ≠ **b. The null and alternative hypotheses would be:** - \( H_0 \): μ = 26 - \( H_1 \): μ ≠ 26 **c. The test statistic \( z \) is:** - [Your answer here, rounded to 3 decimal places] **d. The p-value is:** - [Your answer here, rounded to 4 decimal places] **e. The p-value is:** - ≤ α - > α **f. Based on this, we should:** - Select an answer about the null hypothesis: - Reject - Fail to reject **g. Thus, the final conclusion is:** - The data suggest that the sample mean is not significantly different from 26 at α = 0.10, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is different from 28.1. - The data suggest that the population mean is significantly different from 26 at α = 0.10, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is different from 26. - The data suggest that the population mean is not significantly different from 26 at α = 0.10, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is different from 26. **h. Interpret the p-value in the context of the study.** - There is a 4.25056656% chance that the population mean mpg for your car on the highway is not equal to 26. - If the population mean mpg for your car on the highway is 26 and if you take another 42 trips on the highway, then there would be a 4.25056666% chance that the sample mean for these 42 highway trips would either be less than 24 or greater than 28.1.
Expert Solution
steps

Step by step

Solved in 3 steps with 11 images

Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman