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The quaity control manager at a l ht bub factory needs to estinate the mean ite

ID: 3270837 • Letter: T

Question

The quaity control manager at a l ht bub factory needs to estinate the mean ite of a large shpment ofi a sample mean ie of 470 hours Complete parts (a) through (d) below ht bubs the standard deviation 126 hos A odin sanele arer son bas nears a. Construct a 99% cor Idence interval estimate for the population mean lfe of light bulbs in this shipment The 99% confdence interval estimate is from a lower init 0'hours to an upper Ini!ofhours Round to one decimal place as needed) b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean te of 530 hours? Explain Based ontho sample data the manufacturer the sample man so n is the righe to stahe that the lightbules have a mean iHe of530 hours A mean of 530 hours i standand ers that the Sghtbulbs have a mean ie of 530 hour c. Must you assume that the population 1gh bub u o is normaly distributed? Explain 0 A. Yes the sample siz, istoo lar ge for samping dstrbuson of the mean to be apportately nornal byte Centat Lint oren No since o is known the samping dintation one mean does not need te b-ajpo-mately nama, awened ck to select your Oeeo

Explanation / Answer

given

H0 : = 470

H1 : 470 (claim)

= 0.01 (significance level) = 2.576

std dev=126

n =81

we have formulea is x^+- Za * std /sqrtn

                              470+-2.576*(126/sqrt 81)

                             470+-36.064

                           433.936 ,506.064

so a) lower limit is 433.936 upper limit is 506.064

b) No.The manufacturer cannot support a claim that the bulbs last an average 500 hours. Based on the data from the sample, a mean of 530 hours 2.15 standard error above the sample mean so it is significantally different of 530 hours.

c) option c is correct

d) std =99

we have formulea is x^+- Za * std /sqrtn

                              470+-2.576*(99/sqrt 81)

                              470+-2.576*11

                               470+-28.336

                              441.664,498.336

lower and upper limits

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