Question

Salaries of 34 college graduates who took a statistics course have a mean of $68,700. Assuming a standard deviation of $13,685. Construct a 95% confidence interval for estimating the population mean.

Answer #1

Solution :

Given that,

Point estimate = sample mean =
= 68700

Population standard deviation =
= 13685

Sample size = n = 34

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2
= 0.025

Z/2
= Z0.025 = 1.96

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

= 1.96 * (13685 /
34)

= 2346.96

At 95% confidence interval estimate of the population mean is,

± E

68700 ± 2346.96

(66353.04 , 71046.96)

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