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In: Statistics and Probability

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

An economist wants to estimate the mean per capita income (in thousands of dollars). Suppose that the mean income is found to be $23.4 $23.4 for a random sample of 976 976 people. Assume the population standard deviation is known to be $10 $10. Construct the 95% 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

Answer:

Given that,

= 23.4

= 10

n =976

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95= 0.05

/ 2 = 0.05/ 2 = 0.025

Z/2 = Z0.025= 1.96

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

=1.96 * (10 / 976)

= 0.6274

=0.6

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

- E < < + E

23.4 - 0.6 < < 23.4+ 0.6

22.8< < 24.0

(22.8, 24.0)

orchestra answered 2 years ago
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