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In: Statistics and Probability

The​ quality-control manager at a compact fluorescent light bulb​ (CFL) factory needs to determine whether the...

The​ quality-control manager at a compact fluorescent light bulb​ (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,476 hours. The population standard deviation is1,080 hours. A random sample of 81 light bulbs indicates a sample mean life of 7,176 hours.

a. At the0.05 level of​ significance, is there evidence that the mean life is different from 7,476 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?

A. Let μbe the population mean. Determine the null​ hypothesis, H0​, and the alternative​ hypothesis, H1.

What is the test​ statistic?

What​ is/are the critical​ value(s)?

What is the final​ conclusion?

B. What is the​ p-value? Interpret the meaning of the​ p-value.

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?

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