The owner of a factory wants to determine a confidence interval for the average wages at...

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.

Expert Solution

The formula for confidence interval estimation is:

μ = M ± Z(s_M)

where:

M = sample mean
Z = Z statistic determined by confidence level
s_M = standard error = √(s²/n)

M = 50000
Z = 2.58
s_M = √(3000²/64) = 375

μ = M ± Z(s_M)
μ = 50000 ± 2.58*375
μ = 50000 ± 965.94

99% CI [49034.06, 50965.94].

The Z table used for Z critical value calculation is shown below:

orchestra answered 1 year ago

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