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To estimate LaTeX: \muμ, the mean salary of full professors at American colleges and universities, you obtain the salaries of a random sample of 400 full professors. The sample mean is LaTeX: \bar{x} = $73,220 x ¯ = $ 73 , 220 and the sample standard deviation is s = $4400. A 99% confidence interval for LaTeX: \mu μ is Group of answer choices

A. 73220 +/- 11440

B. 73220 +/- 568

C. 73220 +/- 431

D. 73220 +/- 28.6

Respuesta :

Answer:

99% confidence interval for [tex]\mu = 73220 \pm 565.4[/tex]

Step-by-step explanation:

Sample mean = [tex]\bar{x} =73220[/tex]

Standard deviation = s = 4400

Z at 99%  confidence level = 2.57

Sample = n = 400

Formula of confidence interval :[tex]\bar{x} \pm Z \times \frac{s}{\sqrt{n}}[/tex]

Substitute the values in the formula :

So,99% confidence interval for [tex]\mu = 73220 \pm 2.57 (\frac{4400}{\sqrt{400}})[/tex]

99% confidence interval for [tex]\mu = 73220 \pm 565.4[/tex]

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