#32). This is 1 question. Need help with test statistic and p-value. **Hypothesis Testing Example****Step 1: Determine the Test Statistic**- Compute the test statistic for the given hypothesis test. Round the solution to four decimal places._(Input box for the test statistic will be provided here)_**Step 2: Determine the p-value (range) for the hypothesis test**_(Choose the appropriate range for the p-value from the given options)_- o p-value < 0.0005- o 0.0005 < p-value < 0.005- o 0.005 < p-value < 0.01- o 0.01 < p-value < 0.025- o 0.025 < p-value < 0.05- o 0.05 < p-value < 0.10- o p-value > 0.10**Step 3: Determine the Appropriate Conclusion for this Hypothesis Test**_(Select the conclusion that matches your analysis and p-value)_- o The sample data provide sufficient evidence to reject the null hypothesis that the average range of this electric car is 166 miles and thus we conclude that the true range of the electric car is likely less than 166 miles.- o The sample data do not provide sufficient evidence to reject the null hypothesis that the average range of this electric car is 166 miles and thus we conclude that the true range of the electric car is likely 166 miles.- o The sample data provide sufficient evidence to reject the alternative hypothesis that the average range of this electric car is less than 166 miles and thus we conclude that the true range of this electric car is likely 166 miles.- o The sample data do not provide sufficient evidence to reject the alternative hypothesis that the average range of this electric car is less than 166 miles and thus we conclude that the true range of this electric car is likely less than 166 miles.**Explanation of Steps:**1. **Determine the Test Statistic** - This involves calculating the test statistic based on the sample data and the hypothesis being tested. This value helps in comparing against the critical value to check the validity of the hypothesis.2. **Determine the p-value Range** - The p-value helps in determining the significance of the results obtained. Based on the calculated test statistic, identify the range in which the p-value falls.3. **Draw Conclusions** - Based on the p-value and the significance level (typically 0.05 ## Hypothesis Testing for Electric Vehicle RangeElectric vehicles are often categorized by the range of miles that can be traveled on a single battery charge, since charging stations are not yet widespread in the United States.The latest model of a certain brand of electric car is reported to have an average range of 166 miles.An auto industry journalist would like to verify this claim, since she believes that the true range of the car may be less than 166 miles. The journalist selected and tested a random sample of 107 cars of this model and found that the average range of the sample was 160.3 miles with a standard deviation of 18.2 miles.### Hypothesis Testing**Apply the p-value method to test the hypothesis that the average range of this electric car model is less than 166 miles, using a significance level of 1%.****State the null and alternative hypothesis for this test.**\[H_0: \mu \leq 166\]\[H_1: \mu > 166\]**Determine if this test is left-tailed, right-tailed, or two-tailed.**- [ ] two-tailed- [x] right-tailed- [ ] left-tailed**Should the standard normal (z) distribution or Student’s (t) distribution be used for this test?**- [x] The standard normal (z) distribution should be used- [ ] The Student’s t distribution should be used**Determine the test statistic for the hypothesis test. Round the solution to four decimal places.**\[\text{Test statistic: } \square\]**Determine the p-value (range) for the hypothesis test.**- [ ] p-value < 0.0005- [ ] 0.0005 < p-value < 0.005- [ ] 0.005 < p-value < 0.01- [ ] 0.01 < p-value < 0.025- [ ] 0.025 < p-value < 0.05- [ ] 0.05 < p-value < 0.10- [ ] p-value > 0.10

Given: μ = 166 n = 107 X = 160.3 s = 18.2 α = 0.01 Formula Used: Test-statistic t = X-μsn

Answered: Determine the test statistic for the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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#32). This is 1 question. Need help with test statistic and p-value.

**Hypothesis Testing Example**

**Step 1: Determine the Test Statistic**
- Compute the test statistic for the given hypothesis test. Round the solution to four decimal places.

_(Input box for the test statistic will be provided here)_

**Step 2: Determine the p-value (range) for the hypothesis test**
_(Choose the appropriate range for the p-value from the given options)_

- o p-value < 0.0005
- o 0.0005 < p-value < 0.005
- o 0.005 < p-value < 0.01
- o 0.01 < p-value < 0.025
- o 0.025 < p-value < 0.05
- o 0.05 < p-value < 0.10
- o p-value > 0.10

**Step 3: Determine the Appropriate Conclusion for this Hypothesis Test**
_(Select the conclusion that matches your analysis and p-value)_

- o The sample data provide sufficient evidence to reject the null hypothesis that the average range of this electric car is 166 miles and thus we conclude that the true range of the electric car is likely less than 166 miles.
- o The sample data do not provide sufficient evidence to reject the null hypothesis that the average range of this electric car is 166 miles and thus we conclude that the true range of the electric car is likely 166 miles.
- o The sample data provide sufficient evidence to reject the alternative hypothesis that the average range of this electric car is less than 166 miles and thus we conclude that the true range of this electric car is likely 166 miles.
- o The sample data do not provide sufficient evidence to reject the alternative hypothesis that the average range of this electric car is less than 166 miles and thus we conclude that the true range of this electric car is likely less than 166 miles.

**Explanation of Steps:**

1. **Determine the Test Statistic** - This involves calculating the test statistic based on the sample data and the hypothesis being tested. This value helps in comparing against the critical value to check the validity of the hypothesis.

2. **Determine the p-value Range** - The p-value helps in determining the significance of the results obtained. Based on the calculated test statistic, identify the range in which the p-value falls.

3. **Draw Conclusions** - Based on the p-value and the significance level (typically 0.05

$## Hypothesis Testing for Electric Vehicle Range Electric vehicles are often categorized by the range of miles that can be traveled on a single battery charge, since charging stations are not yet widespread in the United States. The latest model of a certain brand of electric car is reported to have an average range of 166 miles. An auto industry journalist would like to verify this claim, since she believes that the true range of the car may be less than 166 miles. The journalist selected and tested a random sample of 107 cars of this model and found that the average range of the sample was 160.3 miles with a standard deviation of 18.2 miles. ### Hypothesis Testing **Apply the p-value method to test the hypothesis that the average range of this electric car model is less than 166 miles, using a significance level of 1%.** **State the null and alternative hypothesis for this test.** \[ H_0: \mu \leq 166 \] \[ H_1: \mu > 166 \] **Determine if this test is left-tailed, right-tailed, or two-tailed.** - [ ] two-tailed - [x] right-tailed - [ ] left-tailed **Should the standard normal (z) distribution or Student’s (t) distribution be used for this test?** - [x] The standard normal (z) distribution should be used - [ ] The Student’s t distribution should be used **Determine the test statistic for the hypothesis test. Round the solution to four decimal places.** \[ \text{Test statistic: } \square \] **Determine the p-value (range) for the hypothesis test.** - [ ] p-value < 0.0005 - [ ] 0.0005 < p-value < 0.005 - [ ] 0.005 < p-value < 0.01 - [ ] 0.01 < p-value < 0.025 - [ ] 0.025 < p-value < 0.05 - [ ] 0.05 < p-value < 0.10 - [ ] p-value > 0.10$

Transcribed Image Text:## Hypothesis Testing for Electric Vehicle Range Electric vehicles are often categorized by the range of miles that can be traveled on a single battery charge, since charging stations are not yet widespread in the United States. The latest model of a certain brand of electric car is reported to have an average range of 166 miles. An auto industry journalist would like to verify this claim, since she believes that the true range of the car may be less than 166 miles. The journalist selected and tested a random sample of 107 cars of this model and found that the average range of the sample was 160.3 miles with a standard deviation of 18.2 miles. ### Hypothesis Testing **Apply the p-value method to test the hypothesis that the average range of this electric car model is less than 166 miles, using a significance level of 1%.** **State the null and alternative hypothesis for this test.** \[ H_0: \mu \leq 166 \] \[ H_1: \mu > 166 \] **Determine if this test is left-tailed, right-tailed, or two-tailed.** - [ ] two-tailed - [x] right-tailed - [ ] left-tailed **Should the standard normal (z) distribution or Student’s (t) distribution be used for this test?** - [x] The standard normal (z) distribution should be used - [ ] The Student’s t distribution should be used **Determine the test statistic for the hypothesis test. Round the solution to four decimal places.** \[ \text{Test statistic: } \square \] **Determine the p-value (range) for the hypothesis test.** - [ ] p-value < 0.0005 - [ ] 0.0005 < p-value < 0.005 - [ ] 0.005 < p-value < 0.01 - [ ] 0.01 < p-value < 0.025 - [ ] 0.025 < p-value < 0.05 - [ ] 0.05 < p-value < 0.10 - [ ] p-value > 0.10

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