Question

The owner of a factory wants to determine a confidence interval for the average wages at his factory. The population average wages is unknown. However, the owner was able to take a random sample of 64 workers. He found that the average salary for this sample of workers is $50,000. The population standard deviation is $3000. He calculated a 99% confidence interval for the population average wages at the factory. Which of the following choices is correct? Assume the distribution of wages is normally distributed.

Answer 1

4,034.06 ,5,965.94 are confidence interval for the population average wages at the factory.

What is confidence interval estimation?

Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.

                                              If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty.  Another term for probability in statistics is confidence.

The formula for confidence interval estimation is:

μ = M ± Z(sM)

where:

M = sample mean

Z = Z statistic determined by confidence level

sM = standard error = √(s2/n)

M = 50000

Z = 2.58

sM = √(30002/64) = 375

μ = M ± Z(sM)

μ = 50000 ± 2.58*375

μ = 50000 ± 965.94

μ = 4,034.06 ,5,965.94

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