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 7520 hours. The population standard deviation is 840 hours. A random sample of 64 light bulbs indicates a sample mean life of 7,258 hours.

a. At the 0.05 level of​ significance, is there evidence that the mean life is different from 7520 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?

e. Compare the results of parts​ (a) through​ (d) to those when the standard deviation is 1,200 hours.

a. Let μ be the population mean. Determine the null​ hypothesis, H0, and the alternative hypothesis h1

Answer 1

a)

b)The p-value is calculated using excel using the following formula:

2*NORMDIST(-2.495,0,1,1) =0.0126 which is less than 0.05 hence we reject Ho. and conclude that the mean life of bulbs is diiferent from 7520 hours.

c) Confidence Interval

d) Since the population mean of 7520 does not lie in the confidence interval therefore it is concluded that the population mean is different than sample mean. Same result which came from hypothesis testing

e)results for when standard deviation is equal to 1200 hours

The null hypothesis is not rejected.

p value computation:2*NORMDIST(-1.747,0,1,1)=0.0807

Conclusion : Do not reject Ho.p value is which is greater than 0.05 hence we do not reject Ho. and conclude that the mean life of bulbs is not different from 7520 hours.

Confidence Interval:

Since the population mean lies in the confidence Interval therefore we donot reject Ho. Same result.