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# (Solved): he quality-control managet at a compact fuocoscent light bulb (CFL) factory needs to detemine wheth ...

he quality-control managet at a compact fuocoscent light bulb (CFL) factory needs to detemine whether the mean lfe of a large shipmert of CFLs is ecual to 7,495 hours. The poguisios itandwrd evation is 1,080 hours. A rardom sample of 81 light bulbs indicales a sample mean lee of 7,195 hours. 1. At the $$0.05$$ level of significance, is there evidence that the mean Ife is different from $$7.495$$ hours? 2. Compute the p-ralue and interpret its meaning. c. Construct a $$95 \%$$ contidence interval eslimate of the population mean Me of the ligh bulbs. d. Coempare the rewuts of (a) and (c). What conclusions do you reach? a. Let $$\mu$$ bo the populaion moan. Desermine the nuli bypethesis, $$H_{0}$$ i and the atemaive bypolhesis, $$H_{9}$$. $$H_{5}: \mu=$$ $$H_{1}: \mu=$$ What is the test satistic? $$Z_{\text {STAT }}$$ = (Round to two decimal places as needed.) What is are the creical value(s)? (RRound to the iseimw places as needed. Une a cortra to sepsave armats as noosed) What is the fral conckusion? c. Fceject Hy. There a sufficint evidence ss prove thau the mean the is attirent ficm 7 ass tours. D. Fal te reiect Ho. Thare is rot wificert ensence to prove fiat toe maac ale is d feeert bim 7 ass hours What is the p-value? (Round to thes diciral pives as heeded) D. Fal to reject $$\mathrm{H}_{3}$$. Thece is not sufficlent evidence to prove that the mean lite is difterent hom 7,495 hours. b. What is the p-value? (Round ta three decimal places as needed.) Interaret the meaning of the $$\mathrm{p}$$-valoe. Choose the comect answer below. A. Reject $$\mathrm{H}_{0}$$. There is suffident evidence to prove that the mean lilo is ditlerent from 7,495 hour. B. Fal to reject $$\mathrm{H}_{2}$$. There is sutlicient evidecce to prove that the mean Ho is hiflerent fom 7,495 hours. C. Fal to reject $$H_{0}$$. There is not sufficient evidence to prove that the mean Me is daferest from 7,495 hours: D. Fipect $$\mathrm{H}_{0}$$. Hhere is not sufficient evidence to prove that the mean ille is dfferers from $$7,4 \mathrm{PS}$$ hours. c. Corstrust a $$96 \%$$ confidence interval estimate of the pepulation mean ife of the llsht bubt. sps (Round to one decimal place as needed.) d. Compare the resuhs of (a) and (c) What conclsions do you reach? A. The resuls of (a) and $$(c)$$ are the same. there is not sufficient evidence is prove trut the mean ife is dilerent from $$7,4 \% 5$$ houn. b. The resilts of fa) and $$(c)$$, are not the same thare is not sulficient eviderce to pooe that the mean ifte is difierent from $$7.495$$ noars. c. The resuiss of (a) and (c) are the same: there is auficient evidence so prove that the mean ilie is atheienk from 7,495 hours D. The results of (a) and (c) are not bee same: there is suffcont evidence to prove that the mean ide is of Fererk bom $$7.495$$ hours.

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