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Margarita [4]
3 years ago
8

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 $21.1 for a random sample of 717 people. Assume the population standard deviation is known to be $12.6. Construct the 85% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
Mathematics
1 answer:
yuradex [85]3 years ago
5 0

Answer:

The 85% confidence interval for the mean per capita income in thousands of dollars is between $20.4 and $21.8.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.85}{2} = 0.075

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.075 = 0.925, so z = 1.44

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.44\frac{12.6}{\sqrt{717}} = 0.7

The lower end of the interval is the sample mean subtracted by M. So it is 21.1 - 0.7 = $20.4.

The upper end of the interval is the sample mean added to M. So it is 21.1 + 0.7 = $21.8.

The 85% confidence interval for the mean per capita income in thousands of dollars is between $20.4 and $21.8.

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