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 7,543 hours. The population standard deviation is1,080 hours. A random sample of 81 light bulbs indicates a sample means a life of 7,243 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,543 hours?b. Compute the test statistic and critical valuec. Construct a 95%confidence interval estimate of the population mean a life of the light bulbs.d. Compare the results of (a) and (c). What conclusions do you reach? a. Let μ be the population mean. Determine the null hypothesis,H0, and the alternative hypothesis, H1. H0: μ=__H1: μ≠__ b. What is the test statistic and Z critical value? ZSTAT=__(Round to two decimal places as needed.) What is/are the critical value(s)?____ (Round to two decimal places as needed. Use a comma to separate answers as needed.) What is the final conclusion? A. Fail to reject H0. There is not sufficient evidence to prove that the mean life is different from 7,543 hours. B. Fail to reject H0. There is sufficient evidence to prove that the mean life is different from 7,543 hours. C. Reject H0. There is sufficient evidence to prove that the mean life is different from 7,543 hours. D. Reject H0. There is not sufficient evidence to prove that the mean life is different from 7,543 hours. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. __ ≤μ≤ __(Round to one decimal place as needed.) d. Compare the results of (a) and (c). What conclusions do you reach? A.The results of (a) and (c) are not the same: there is sufficient evidence to prove that the mean life is different from 7,543 hours. B. The results of (a) and (c) are the same: there is not sufficient evidence to prove that the mean life is different from 7,543 hours. C. The results of (a) and (c) are the same: there is sufficient evidence to prove that the mean life is different from 7,543 hours. D. The results of (a) and (c) are not the same: there is not sufficient evidence to prove that the mean life is different from 7,543 hours.

Name: The quality-control manager at a compact fluorescent light bulb (CFL
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: 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 7,543 hours. The population standard deviation is1,080 hours. A random sample of 81 light

Question

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 7,543 hours. The population standard deviation is1,080 hours. A random sample of 81 light bulbs indicates a sample means a life of 7,243 hours. a. At the 0.05 level of​ significance, is there evidence that the mean life is different from 7,543 hours?b. Compute the test statistic and critical valuec. Construct a 95​%confidence interval estimate of the population mean a life of the light bulbs.d. Compare the results of​ (a) and​ (c). What conclusions do you​ reach? a. Let μ be the population mean. Determine the null​ hypothesis,H0​, and the alternative​ hypothesis, H1. H0​: μ=__H1​: μ≠__ b. What is the test statistic and Z critical​ value? ZSTAT=__​(Round to two decimal places as​ needed.) What​ is/are the critical​ value(s)?____ ​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.) What is the final​ conclusion? A. Fail to reject H0. There is not sufficient evidence to prove that the mean life is different from 7,543 hours. B. Fail to reject H0. There is sufficient evidence to prove that the mean life is different from 7,543 hours. C. Reject H0. There is sufficient evidence to prove that the mean life is different from 7,543 hours. D. Reject H0. There is not sufficient evidence to prove that the mean life is different from 7,543 hours.  c. Construct a​ 95% confidence interval estimate of the population mean life of the light bulbs. __ ≤μ≤ __​(Round to one decimal place as​ needed.) d. Compare the results of​ (a) and​ (c). What conclusions do you​ reach? A.The results of​ (a) and​ (c) are not the​ same: there is sufficient evidence to prove that the mean life is different from 7,543 hours. B. The results of​ (a) and​ (c) are the​ same: there is not sufficient evidence to prove that the mean life is different from 7,543 hours. C. The results of​ (a) and​ (c) are the​ same: there is sufficient evidence to prove that the mean life is different from 7,543 hours. D. The results of​ (a) and​ (c) are not the​ same: there is not sufficient evidence to prove that the mean life is different from 7,543 hours.

Accepted Answer

Solution:
Given:
Sample mean is = x= 7243 and the known population standard deviation is σ = 1080…