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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 $23.6$⁢23.6 for a random sample of 12341234 people. Assume the population standard deviation is known to be $11.4$⁢11.4. Construct the 90%90% 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

ANSWER:

Given that,

= 23.6

= 11.4

n =1234

At 90% confidence level the z is ,

  = 1 - 90% = 1 - 0.90=0.10

Z/2 = 1.645

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

=1.645 * (11.4 / 1234)

= 0.5

At 90% confidence interval estimate of the population mean is,

- E < < + E

23.6 - 0.5 < < 23.6 + 0.5

23.1< < 24.1

(23.1,24.1 )

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orchestra answered 2 years ago
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