Question

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 Texas. Suppose that the mean income is found to be $21.8 for a random sample of 1691 people. Assume the population standard deviation is known to be $9.8. Construct the 99% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place

Homework Answers

Answer #1

Sample size = n = 1691

Sample mean = = 21.8

Population standard deviation = = 9.8

We have to construct 99% confidenc interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 2.58    ( Using z table)

So confidence interval is ( 21.8 - 0.6149 , 21.8 + 0.6149) = > ( 21.2 , 22.4)

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