The quality-control manager at a compact fluorescent light bulb (CFL) factory ne

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 7,464 hours. The population standard deviation is 900 hours. A random sample of 81 light bulbs indicates a sample mean life of 7,214 hours.

a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,464 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 be the population mean. Determine the null hypothesis, H0, and the alternative hypothesis, H1.

H0: =

H1:

Explanation / Answer

a)H0: = 7464

H1: 7464

here std error =std deviation/(n)1/2 =100

hebce test stat z=(X-mean)/std error =(7214-7464)/100=-2.5

for above p value =0.0124 which gives extreme probability to accept null hypothesis given it is right

as p value is less then 0.05 level we reject null hypothesis and conclude that there is sufficient evidence that the mean life is different from 7,464 hours

c) for 95% CI, z=1.96

hence 95% confidence interval =sample mean -/+ z*std errror =7214-/+ 1.96*100 =70.18.004 ; 7409.996

d) from above as our confidence interval does not contain 7464 as probable value of true mean life we reject null hypothesis and conclude that there is sufficient evidence that the mean life is different from 7,464 hours

Hence result from both a and c are same

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