A city has 10,000 households, and you have collected a simple random sample size of 25...

A city has 10,000 households, and you have collected a simple random sample size of 25 from the households in this city and measured how much each household paid in school taxes in 2012. For this sample, X = $2500, and s = $ 1000. You wish to construct a 95% confidence interval for μ.

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Expert Solution

Solution :

Given that,

sample mean = = $2500

sample standard deviation = s = $1000

sample size = n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = 0.025 , 24 = 2.064

Margin of error = E = t_/2,df * (s / $\sqrt$ n)

= 2.064* (1000 / $\sqrt$ 25)

Margin of error = E =412.8

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

- E < < + E

2500 - 412.8 < < 2500 +412.8

2087.2 < < 2912.8

(2087.2 , 2912.8)

milcah answered 10 months ago

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