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alex41 [277]
3 years ago
15

Suppose that you want to estimate average income in a population. If the standard deviation of income in the population is $1,00

0, approximately how many people do you need to sample in order to have a 95% confidence interval around your estimate of +/- $40?*
Mathematics
1 answer:
Alik [6]3 years ago
3 0

Answer:

2401

Step-by-step explanation:

Given that we want to estimate average income in a population.

The standard deviation of income in the population is $1,000

We want confidence interval around our estimate to be +/- $40

i.e Margin of error = 40

We know that margin of error = Std error * Z critical for 95%

i.e. 40 = 1.96 * std error

Std error = \frac{std dev}{\sqrt{n} } \\=\frac{1000}{\sqrt{n} }

Together we get

40=1.96(\frac{1000}{\sqrt{n} } )\\\sqrt{n} =\frac{1000*1.96}{40} \\=49\\n=2401\\

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