Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of forty hours. If a sample of thirty bulbs has an average life of 800 hours, find a 95% confidence interval for the population mean of all bulbs produced by this firm.

I am pretty sure this is a estimating a population proportion question. i am just not sure how to do it with the supplied information. any help would be appreciated.

Answer 1

For starters: you are estimating a population PARAMETER, but this parameter is not the population proportion. The problem statement mentions population standard deviation. This is your clue that we are estimating the population (what?).

Are you familiar with the formula for the confidence interval estimating that parameter?

If so, please type it in.

Here I observe that n (the sample size) is 30, the population standard deviation is (capitalized Greek letter) "sigma"), and the desired level of confidence is 95%. What is the "z critical value" corresponding to that level of confidence?

Answer 2

i do not know the population parameter formula. but the z score for 95% is 1.96

Answer 3

Silver: in this statistics course, we are either estimating the population proportion or the population mean when we set up a confidence interval.

The problem you're trying to solve has the words "average" and "standard deviation," implying that we're aiming to estimate the population parameter mu (Greek letter), which is the population mean.

If the sample mean is given and is 800, then we can take the population mean, mu, to be 800 also. With the same mean = x bar = 800, the population standard deviation = capital sigma = 40 (given), we calculate the SAMPLE standard deviation (= S) as (population standard deviation / sqrt(sample size), or S = (capital sigma) / Sqrt(n). Here, S = 40/Sqrt(30).

Then the formula to evaluate to create the desired confidence interval becomes:

(x bar) (plus or minus) (z-critical value)*(sample standard deviation);

here that comes out to 800 (plus or minus) 1.96 (as you say) times (40/Sqrt(30)).

Try evaluating this and writing the confidence interval.

Note that the quantity 1.96 times (40/Sqrt(30)) is called the "margin of error."

Good luck!