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Ad libitum [116K]
3 years ago
12

A researcher wants to estimate the mean age of all Business Week readers at a 99% confidence level. The standard deviation of ag

es of all Business Week readors is nine years. The sample size that will yield a maximum error of estimate within three years of the population mean is at least:
A. 60
B. 97
C. 185
D. 8
Mathematics
1 answer:
Natasha2012 [34]3 years ago
5 0

Answer:

A. 60

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{1-0.99}{2} = 0.005

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 1-0.005 = 0.995, so z = 2.575

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.

We have to find:

n when M = 3, \sigma = 9. So

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

3 = 2.575*\frac{9}{\sqrt{n}}

3\sqrt{n} = 9*2.575

Dividing both sides by 3

\sqrt{n} = 3*2.575

(\sqrt{n})^{2} = (3*2.575)^{2}

n = 59.68

We round up, so the correct answer is:

A. 60

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