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In: Statistics and Probability

An economist wants to estimate the mean per capita income (in thousands of dollars) for a...

An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $23.1 for a random sample of 3231 people. Assume the population standard deviation is known to be $11.8. Construct the 95% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.

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Expert Solution

Solution :  

Given that,

= 23.1

= 11.8

n = 3231

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.960 * (11.8 / 3231 )

= 0.4

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

- E < < + E

23.1 - 0.4 < < 23.1 + 0.4

22.7 < < 23.5

( 22.7, 23.5 )

orchestra answered 1 year ago
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