Question

TThe quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 108 hours. A random sample of 81 light bulbs indicated a sample mean life of 410 hours . a. Construct a 99% confidence interval estimate for the population mean life of light bulbs in this shipment. b. Do you think that the manufacturer has the right to state that the light bulbs have a mean life of 410 hours? Explain. c. Must you assume that the population light bulb life is normally distributed? Explain. d. Suppose that the standard deviation changes to 80 hours. What are your answers in (a) and (b)?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 410

Population standard deviation =    = 108

Sample size = n =81

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( /n)

= 2.576 * (108 / 81)

= 30.9120

At 99% confidence interval estimate of the population mean is,

- E < < + E

140 - 30.9120< < 140 +30.9120

109.088< < 170.9120

(109.088 , 170.9120 )

b.Do you think that the manufacturer has the right to state that the light bulbs have a mean life of 410 hours = yes

c.Must you assume that the population light bulb life is normally distributed = yes

d. Suppose that the standard deviation changes to 80 hours. yes any time change