Suppose a certain type of 40watt bulb has been standardized

Suppose a certain type of 40-watt bulb has been standardized so that the mean life of the bulb is 1500 hours and the population standard deviation is 200 hours. A random sample of 40 of these bulbs from the same lot
were tested and found to have a mean life of 1380 hours.

(a) Determine the 98% confidence interval for the true mean of this lot.
(b) Does the company actually sell bulbs with a mean life of less than1500 hours? Use a hypothesis test with significance level of

Solution

(a)

For 98% confidence interval ,

Margin of error = (z * sigma)/sqrt(n)

                      = ( 2.33 * 200 ) /sqrt( 40)

                      = 73.68

Therefore Confidence interval CI

= ( 1380 - 73.68 , 1380 + 73.68)

= ( 1306.32 , 1453.68 ) Answer

(b)

t = (1380 - 1500) / (200/sqrt(40))

= -3.79

Therefore P-value = 0.0002

which is less than 0.1.

Hence significant , and so the company actually sell bulbs with a mean life of less than 1500 hours.