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Helen [10]
3 years ago
6

The population standard deviation for the typing speeds for secretaries is 4 words per minute. If we want to be 90% confident th

at the sample mean is within 1 word per minute of the true population mean, what is the minimum sample size that should be taken
Mathematics
1 answer:
Oksana_A [137]3 years ago
8 0

Answer:

The minimum sample size that should be taken is 62.

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{1-0.9}{2} = 0.05

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 1-0.05 = 0.95, so z = 1.645

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.

If we want to be 90% confident that the sample mean is within 1 word per minute of the true population mean, what is the minimum sample size that should be taken

This is n when M = 1, \sigma = 4. So

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

1 = 1.96*\frac{4}{\sqrt{n}}

\sqrt{n} = 4*1.96

(\sqrt{n})^{2} = (4*1.96)^{2}

n = 61.5

The minimum sample size that should be taken is 62.

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