A manufacturer claims that the mean lifetime, u, of its light bulbs is 55 months. The standard deviation of these lifetimes is 9 months. Eighty bulbs are selected at random, and their mean lifetime is found to be 54 months, Can we conclude, at the 0.10 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 55 months? Perform a two-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 H, and the alternative hypothesis H. H, : H :0 (b) Determine the type of test statistic to use. O=0 OSO (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values. (Round to three or more decimal places.) I and (e) Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 55 months? OYes ONo Ix
A manufacturer claims that the mean lifetime, u, of its light bulbs is 55 months. The standard deviation of these lifetimes is 9 months. Eighty bulbs are selected at random, and their mean lifetime is found to be 54 months, Can we conclude, at the 0.10 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 55 months? Perform a two-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 H, and the alternative hypothesis H. H, : H :0 (b) Determine the type of test statistic to use. O=0 OSO (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values. (Round to three or more decimal places.) I and (e) Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 55 months? OYes ONo Ix
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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![**Hypothesis Testing of Light Bulb Lifetimes**
A manufacturer claims that the mean lifetime, \( \mu \), of its light bulbs is 55 months. The standard deviation of these lifetimes is 9 months. A sample of 80 bulbs is selected randomly, and their mean lifetime is found to be 54 months. At the 0.10 level of significance, can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 55 months?
**Perform a two-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 \( H_0 \) and the alternative hypothesis \( H_1 \).**
- \( H_0: \)
- \( H_1: \)
(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 two critical values.** (Round to three or more decimal places.)
- [ ] and [ ]
(e) **Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 55 months?**
- [ ] Yes
- [ ] No
**Explanation:**
- **Graphical Components:** The image includes symbols and icons representing statistical measures, commonly used in hypothesis testing—such as \( \mu \), \( \sigma \), and choices for test statistics. There are entry fields for recording hypotheses, selecting test statistics, calculating values, and making conclusions.
This task involves setting hypotheses, selecting an appropriate statistical test, computing a test statistic and critical values, and making an inference based on the calculated data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d3f2bfb-a5cc-4b06-99e2-b36f9d38db79%2F57882b7d-0636-4f00-a9ee-7c881094525a%2Fskt7uy8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing of Light Bulb Lifetimes**
A manufacturer claims that the mean lifetime, \( \mu \), of its light bulbs is 55 months. The standard deviation of these lifetimes is 9 months. A sample of 80 bulbs is selected randomly, and their mean lifetime is found to be 54 months. At the 0.10 level of significance, can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 55 months?
**Perform a two-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 \( H_0 \) and the alternative hypothesis \( H_1 \).**
- \( H_0: \)
- \( H_1: \)
(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 two critical values.** (Round to three or more decimal places.)
- [ ] and [ ]
(e) **Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 55 months?**
- [ ] Yes
- [ ] No
**Explanation:**
- **Graphical Components:** The image includes symbols and icons representing statistical measures, commonly used in hypothesis testing—such as \( \mu \), \( \sigma \), and choices for test statistics. There are entry fields for recording hypotheses, selecting test statistics, calculating values, and making conclusions.
This task involves setting hypotheses, selecting an appropriate statistical test, computing a test statistic and critical values, and making an inference based on the calculated data.
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