The manufacturer claims that your new car gets 26 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 standard deviation for these 42 trips was 6.5 mpg. What can be concluded at the a = 0.10 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? H₁: ? Select an answer Select an answer c. The test statistic ?✔ = d. The p-value = e. The p-value is 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.) 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 population mean is significantly different from 26 at x = 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 from 26.

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Need help with C and D please

**Hypothesis Testing for Car Mileage on Highway**

**Scenario:**
The car manufacturer claims that your new car achieves 26 miles per gallon (mpg) on the highway. You suspect a different mpg based on your observation. After 42 highway trips, you recorded an average of 28.1 mpg with a standard deviation of 6.5 mpg. You want to test at a significance level of \(\alpha = 0.10\).

**Steps for Hypothesis Testing:**

a. **Study Selection:**
   - Choose between one-sample \(z\) or \(t\) test.

b. **Define Hypotheses:**
   - Null Hypothesis (\(H_0\)): The population mean mpg on the highway is 26.
   - Alternative Hypothesis (\(H_1\)): The population mean mpg on the highway is different from 26.

c. **Test Statistic Calculation:**
   - Compute the test statistic value and report it to 3 decimal places.

d. **p-Value Calculation:**
   - Calculate the p-value and report it to 4 decimal places.

e. **Compare p-Value and Significance Level:**
   - Determine if p-value \(\leq \alpha\) or not.

f. **Conclusion:**
   - Choose from:
     1. Insignificant evidence; mpg not significantly different from 26.
     2. Significant evidence; mpg significantly different from 26.

g. **Interpretation of the p-Value:**
   - Explain the percentage chance that the population mean mpg is not equal to 26 using the p-value.

h. **Interpretation of Significance Level:**
   - Explain the level of significance and the chance of committing a Type I error.

This guide will aid in evaluating the mpg claim at the specified significance level and understanding the statistical evidence regarding your car's highway fuel efficiency.
Transcribed Image Text:**Hypothesis Testing for Car Mileage on Highway** **Scenario:** The car manufacturer claims that your new car achieves 26 miles per gallon (mpg) on the highway. You suspect a different mpg based on your observation. After 42 highway trips, you recorded an average of 28.1 mpg with a standard deviation of 6.5 mpg. You want to test at a significance level of \(\alpha = 0.10\). **Steps for Hypothesis Testing:** a. **Study Selection:** - Choose between one-sample \(z\) or \(t\) test. b. **Define Hypotheses:** - Null Hypothesis (\(H_0\)): The population mean mpg on the highway is 26. - Alternative Hypothesis (\(H_1\)): The population mean mpg on the highway is different from 26. c. **Test Statistic Calculation:** - Compute the test statistic value and report it to 3 decimal places. d. **p-Value Calculation:** - Calculate the p-value and report it to 4 decimal places. e. **Compare p-Value and Significance Level:** - Determine if p-value \(\leq \alpha\) or not. f. **Conclusion:** - Choose from: 1. Insignificant evidence; mpg not significantly different from 26. 2. Significant evidence; mpg significantly different from 26. g. **Interpretation of the p-Value:** - Explain the percentage chance that the population mean mpg is not equal to 26 using the p-value. h. **Interpretation of Significance Level:** - Explain the level of significance and the chance of committing a Type I error. This guide will aid in evaluating the mpg claim at the specified significance level and understanding the statistical evidence regarding your car's highway fuel efficiency.
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