Question

an electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. the firm claims that the mean life of the light bulb is 800 hrs

a?if a sample of 30 light bulbs were tested to failure and had an avg life of 780 hours, find 90% confidence interval on the mean

b) based on this confidence interval, would you be able to validate the claimed mean life of 800 hrs?

c) how large a sample is needed if we wish to be 90% confident that our sample mean will be within 20 hrs of the true mean?

Answer 1

a)

90% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

780 - 1.645 * 40 / sqrt(30) < < 780 + 1.645 * 40 / sqrt(30)

767.99 < < 792.01

90% CI for is ( 767.99 , 792.01 )

b)

Since 800 not contained in confidence interval, we have enough evidence to support the alternative claim that

mean life is not 800.

c)

Sample size = ( Z * / E)²

= ( 1.645 * 40 / 20)²

= 10.82

Sample size = 11 (Rounded up to nearest integer).