Question

A company has developed a new type of light bulb, and wants to estimate its mean

lifetime. A simple random sample of 12 bulbs had a sample mean lifetime of 665

hours with a sample standard deviation of 59 hours. It is reasonable to believe that

the population is approximately normal. Find the lower bound of the 95% confidence

interval for the population mean lifetime of all bulbs manufactured by this new

process.


Round to the nearest integer. Write only a number as your answer. Do not write any

units.

Answer 1

628

Explanation:

We have the standard deviation of the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 12 - 1 = 11

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.95)/(2) = 0.975`. So we have T = 2.2

The margin of error is:

`M = T(s)/(√(n)) = 2.2(59)/(√(12)) = 37`

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 665 - 37 = 628 hours.

The answer is 628