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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? 
 

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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