Next Question ,507 hours. The population standard deviation is 700 hours. A random The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment 49 light bulbs indicates a sample mean life of 7,357 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,507 hours? b. Compute the p-value and interpret its meaning. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. d. Compare the results of (a) and (c). What conclusions do you reach?

MATLAB: An Introduction with Applications
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The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of light bulbs is 7,507 hours. The population standard deviation is 700 hours. A random sample of 49 light bulbs indicates a sample mean life of 7,357 hours.

a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,507 hours?

b. Compute the p-value and interpret its meaning.

c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.

d. Compare the results of (a) and (c). What conclusions do you reach?

Explanation:

- **No graphs or diagrams are present in this text.** 
- The text is structured as a problem set with four parts, guiding the reader through a statistical hypothesis testing process. 
- It involves checking the significance of the difference between a sample mean and a population mean, calculating p-values, and constructing confidence intervals.
- The context focuses on quality control in a manufacturing setting, specifically related to the lifespan of light bulbs.
Transcribed Image Text:The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of light bulbs is 7,507 hours. The population standard deviation is 700 hours. A random sample of 49 light bulbs indicates a sample mean life of 7,357 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,507 hours? b. Compute the p-value and interpret its meaning. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. d. Compare the results of (a) and (c). What conclusions do you reach? Explanation: - **No graphs or diagrams are present in this text.** - The text is structured as a problem set with four parts, guiding the reader through a statistical hypothesis testing process. - It involves checking the significance of the difference between a sample mean and a population mean, calculating p-values, and constructing confidence intervals. - The context focuses on quality control in a manufacturing setting, specifically related to the lifespan of light bulbs.
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