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The quality-control manager, needs to determine whether the mean life of a large shipment of CFLs is equals to 7,508 hrs

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Asked: Jan 23,2019 In: Confidence intervals
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Asked: Jan 23,2019 In: Confidence intervals

The quality-control manager, needs to determine whether the mean life of a large shipment of CFLs is equals to 7,508 hrs

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 7,508 hours. The population standard deviation is 840 hours. A random sample of 49 light bulbs indicates a sample mean life of 7,328 hours.

a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,508 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 
d. Compare the results of (a) and (c). What conclusions do you reach?

What is the final conclusion? 
 


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tutor Added an answer on Jun 04,2019

Statistical hypothesis testing using the z-statistic because the population standard deviation has been given. This is a two-tailed test as it can be seen that the claim does not specify the direction of the claim. 

z - statistic  = (x_bar  - mu)/(sigma/sqrt(n))

z-statistic = (7328 - 7508)/(840/sqrt(49)) = -1.5

Obtain the p -value for the two-tailed test statistic, =NORM.S.DIST(-1.5,TRUE)   = 0.0668

the  p value  = 0.0668 * 2 = 0.1336, 

Do not reject the null hypothesis, because the p-value (0.1336) is greater than the value of alpha. 

Procedure for constructing the 95% confidence interval is, x_bar +/- 1.96 * 840/sqrt(49) 

7328  +/- 1.96 * 840/sqrt(49) 

95% confidence interval = (7328 +/- 235.2), 95 percent confidence interval = (7092.8, 7563.2)

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