SELF 9.14 The quality-control manager at a compact flu- orescent light bulb (CFL

Question

SELF 9.14 The quality-control manager at a compact flu- orescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,500 hours. The population standard deviation is 1,000 hours. A random sample of 64 CFLs indicates a sample mean life of nt 7,250 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,500 hours? b. Compute the p-value and interpret its meaning. c. Construct a 95% confidence interval estimate of the population mean life of the CFLs d. Compare the results of (a) and (c). What conclusions do you ach? Suppose that in Problem 9.14, the standard deviation is 1,200 hou

Explanation / Answer

Ans:

a)population standard deviation=1200

Test statistic:

z=(7250-7500)/(1200/sqrt(64))

z=-1.67

critical z values=-1.96 and +1.96

As test statistic z does not fall in rejection region,we fail to reject null hypothesis.

There is insufficient evidence to conclude that mean life is different from 7500.

b)

p-value(2 tailed)=2*P(z<-1.67)=0.0955

p-value>0.05,we fail to reject the null hypothesis.

c)

95% confidence interval for popualtion mean

=7250+/-1.96*(1200/sqrt(64))

=7250+/-294

=(6956, 7544)

d)As above Confidence interval contains 7500 within its limits,population mean is not different from 7500.

(conclusion for part a and c are same)

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