cording to a leasing firm's reports, the mean number of miles driven annually in its leased cars is 12,920 miles with a standard deviation of 2280 miles. The ompany recently starting using new contracts which require customers to have the cars serviced at their own expense. The company's owner believes the mean umber of miles driven annually under the new contracts, μ, is less than 12,920 miles. He takes a random sample of 80 cars under the new contracts. The cars in the sample had a mean of 12,842 annual miles driven. Is there support for the claim, at the 0.05 level of significance, that the population mean number of miles driven annually by cars under the new contracts, is less than 12,920 miles? Assume that the population standard deviation of miles driven annually was not affected by the change to the contracts. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) state the null hypothesis Ho and the alternative hypothesis H₁. Ho :O H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the claim that the population mean number of miles driven annually by cars under the new contracts is less than 12,920 miles? OYes O No R I Ix D X S p 00 0=0 OSO O
cording to a leasing firm's reports, the mean number of miles driven annually in its leased cars is 12,920 miles with a standard deviation of 2280 miles. The ompany recently starting using new contracts which require customers to have the cars serviced at their own expense. The company's owner believes the mean umber of miles driven annually under the new contracts, μ, is less than 12,920 miles. He takes a random sample of 80 cars under the new contracts. The cars in the sample had a mean of 12,842 annual miles driven. Is there support for the claim, at the 0.05 level of significance, that the population mean number of miles driven annually by cars under the new contracts, is less than 12,920 miles? Assume that the population standard deviation of miles driven annually was not affected by the change to the contracts. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) state the null hypothesis Ho and the alternative hypothesis H₁. Ho :O H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the claim that the population mean number of miles driven annually by cars under the new contracts is less than 12,920 miles? OYes O No R I Ix D X S p 00 0=0 OSO O
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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Question
![### Hypothesis Testing: Mileage Example
According to a leasing firm's reports, the mean number of miles driven annually in its leased cars is 12,920 miles with a standard deviation of 2,280 miles. The company recently started using new contracts which require customers to have the cars serviced at their own expense. The company's owner believes the mean number of miles driven annually under the new contracts, \(\mu\), is less than 12,920 miles. To test this claim, a random sample of 80 cars under the new contracts showed a mean of 12,842 annual miles driven.
**Objective:** Test the claim, at a 0.05 level of significance, that the population mean number of miles driven annually by cars under the new contracts is less than 12,920 miles. Assume the population standard deviation of miles driven annually was not affected by the change to the contracts.
### Procedure
#### (a) State the Hypotheses:
- Null Hypothesis (\(H_0\)): \(\mu \geq 12,920\)
- Alternative Hypothesis (\(H_1\)): \(\mu < 12,920\)
#### (b) Determine the Type of Test Statistic:
- Choose: Z-test (since we know the population standard deviation and the sample size is large)
#### (c) Find the Value of the Test Statistic:
- Use the formula for the Z-test statistic:
\[
Z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
where:
\(\bar{x} = 12,842\),
\(\mu = 12,920\),
\(\sigma = 2,280\),
\(n = 80\).
#### (d) Find the p-value:
- Compute the p-value corresponding to the calculated Z value.
#### (e) Conclusion:
- Can we support the claim that the population mean number of miles driven annually by cars under the new contracts is less than 12,920 miles?
- Check the result: [Yes] or [No]
### Note:
Carry your intermediate computations to three or more decimal places, and round your responses as specified. If necessary, consult a list of formulas or a standard Z-table for reference.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc76302d8-8316-4723-aa90-6b1c8383fd94%2Fcc662fad-dbde-4b94-9a3d-6c9fed7b3e32%2Fgaao47p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing: Mileage Example
According to a leasing firm's reports, the mean number of miles driven annually in its leased cars is 12,920 miles with a standard deviation of 2,280 miles. The company recently started using new contracts which require customers to have the cars serviced at their own expense. The company's owner believes the mean number of miles driven annually under the new contracts, \(\mu\), is less than 12,920 miles. To test this claim, a random sample of 80 cars under the new contracts showed a mean of 12,842 annual miles driven.
**Objective:** Test the claim, at a 0.05 level of significance, that the population mean number of miles driven annually by cars under the new contracts is less than 12,920 miles. Assume the population standard deviation of miles driven annually was not affected by the change to the contracts.
### Procedure
#### (a) State the Hypotheses:
- Null Hypothesis (\(H_0\)): \(\mu \geq 12,920\)
- Alternative Hypothesis (\(H_1\)): \(\mu < 12,920\)
#### (b) Determine the Type of Test Statistic:
- Choose: Z-test (since we know the population standard deviation and the sample size is large)
#### (c) Find the Value of the Test Statistic:
- Use the formula for the Z-test statistic:
\[
Z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
where:
\(\bar{x} = 12,842\),
\(\mu = 12,920\),
\(\sigma = 2,280\),
\(n = 80\).
#### (d) Find the p-value:
- Compute the p-value corresponding to the calculated Z value.
#### (e) Conclusion:
- Can we support the claim that the population mean number of miles driven annually by cars under the new contracts is less than 12,920 miles?
- Check the result: [Yes] or [No]
### Note:
Carry your intermediate computations to three or more decimal places, and round your responses as specified. If necessary, consult a list of formulas or a standard Z-table for reference.
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