An electronics manufacturing process has historically had a mean completion time of 65 minutes. It is claimed that, due to improvements in the process, the mean completion time, μ, is now less than 65 minutes. A random sample of 22 completion times using the new process is taken. The sample has a mean completion time of 59 minutes, with a standard deviation of 12 minutes. Assume that completion times using the new process are approximately normally distributed. At the 0.05 level of significance, can it be concluded that the population mean completion time using the new process is less than 65 minutes? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H₂ :O H₁ :0 (6) μ |x 11 0 S Р
An electronics manufacturing process has historically had a mean completion time of 65 minutes. It is claimed that, due to improvements in the process, the mean completion time, μ, is now less than 65 minutes. A random sample of 22 completion times using the new process is taken. The sample has a mean completion time of 59 minutes, with a standard deviation of 12 minutes. Assume that completion times using the new process are approximately normally distributed. At the 0.05 level of significance, can it be concluded that the population mean completion time using the new process is less than 65 minutes? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H₂ :O H₁ :0 (6) μ |x 11 0 S Р
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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![### Hypothesis Testing for Mean Completion Time
An electronics manufacturing process has historically had a mean completion time of 65 minutes. It is claimed that due to improvements in the process, the mean completion time \(\mu\) is now less than 65 minutes. A random sample of 22 completion times using the new process is taken. The sample has a mean completion time of 59 minutes, with a standard deviation of 12 minutes.
Assume that completion times using the new process are approximately normally distributed. At the 0.05 level of significance, can it be concluded that the population mean completion time using the new process is less than 65 minutes?
**Perform a one-tailed test.** Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
#### Steps:
(a) **State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \)**
- \( H_0 : \mu = 65 \)
- \( H_1 : \mu < 65 \)
(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 critical value.** (Round to three or more decimal places.)
- [ ]
(e) **Conclusion**
Can it be concluded that the mean completion time using the new process is less than 65 minutes?
- [ ] Yes
- [ ] No
#### Diagram Explanation:
The diagram on the right is a visual aid that includes different statistical symbols and icons typically used in hypothesis testing, such as:
- \( \mu \) for population mean
- \( \sigma \) for population standard deviation
- Various test statistic symbols and comparison icons to aid in selecting the appropriate test and calculating critical values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9aa8b2c-c466-4915-a4bd-112cc31f9857%2F93254003-771d-493e-b61f-ee6c9239858e%2Flxbef5m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Mean Completion Time
An electronics manufacturing process has historically had a mean completion time of 65 minutes. It is claimed that due to improvements in the process, the mean completion time \(\mu\) is now less than 65 minutes. A random sample of 22 completion times using the new process is taken. The sample has a mean completion time of 59 minutes, with a standard deviation of 12 minutes.
Assume that completion times using the new process are approximately normally distributed. At the 0.05 level of significance, can it be concluded that the population mean completion time using the new process is less than 65 minutes?
**Perform a one-tailed test.** Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
#### Steps:
(a) **State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \)**
- \( H_0 : \mu = 65 \)
- \( H_1 : \mu < 65 \)
(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 critical value.** (Round to three or more decimal places.)
- [ ]
(e) **Conclusion**
Can it be concluded that the mean completion time using the new process is less than 65 minutes?
- [ ] Yes
- [ ] No
#### Diagram Explanation:
The diagram on the right is a visual aid that includes different statistical symbols and icons typically used in hypothesis testing, such as:
- \( \mu \) for population mean
- \( \sigma \) for population standard deviation
- Various test statistic symbols and comparison icons to aid in selecting the appropriate test and calculating critical values.
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