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 7,527 hours. The population standard deviation is 840 hours. A random sample of 49 light bulbs indicates a sample mean life of7,347 hours.

a. At the 0.05 level of​ significance, is there evidence that the mean life is different from 7,527 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?

Answer 1

Using excel<data<megastat<hypothesis test

Hypothesis Test: Mean vs. Hypothesized Value
	7,527.00	hypothesized value
	7,347.00	mean 1
	840.00	std. dev.
	120.00	std. error
	49	n
	-1.50	z
	.1336	p-value (two-tailed)
	7,111.80	confidence interval 95.% lower
	7,582.20	confidence interval 95.% upper

a) Test statistic z=-1.50

Critical value = -1.96 and 1.96

Reject H0 if z < -1.96 0r z > 1.96

Fail to reject H0. There is not sufficient evidence to prove the claim that the mean life is different from 7527.

b) p-value = 0.1336

P-value = 0.1336 indicated the probability of sample means a life of shipment is equal to 7454

c)

Confidence interval =(7111.80,7582.20)

d)

Conclusions are same from a) and c) Fail to reject H0

There is not sufficient evidence to prove the claim that the mean life is different from 7527.

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