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Starting salaries of 64 college graduates who have taken a statistics course have a mean of...

Starting salaries of 64 college graduates who have taken a statistics course have a mean of $44,500 with a standard deviation of $6,800. Find a 99.7% confidence interval for μ. (NOTE: Do not use commas or dollar signs in your answers. Round each bound to three decimal places.)

Lower bound: Upper bound:

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Answer #1

Solution :

Given that,

Point estimate = sample mean = = $44500

Population standard deviation =    = $6800
Sample size = n =64

At 99.7% confidence level the z is ,

= 1 - 99.7% = 1 - 0.997 = 0.003

/ 2 = 0.003 / 2 = 0.0015

Z/2 = Z0.0015 = 2.97


Margin of error = E = Z/2 * ( /n)

= 2.97 * ( 6800 /  64 )

= 2524.5
At 99.7% confidence interval estimate of the population mean
is,

- E < < + E

44500 - 2524.5 <   < 44500 + 2524.5

41975.500 <   < 47024.500

( 41975.500 ,47024.500)

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