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The population standard deviation for the weights of boxes of breakfast cereal is 0.6 ounces. If we want to be 90% confident that the sample mean is within 1 ounce of the true population mean, what is the minimum sample size that can be taken

User Sharpiro
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1 Answer

3 votes

Answer:

The minimum sample size that can be taken is 1.

Explanation:

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


\alpha = (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*(\sigma)/(√(n))

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

In this problem

We have to find n, when
M = 1, \sigma = 0.6. So


M = z*(\sigma)/(√(n))


1 = 1.645*(0.6)/(√(n))


√(n) = 1.645*0.6


(√(n))^(2) = (1.645*0.6)^(2)


n = 0.97

Rounding up

The minimum sample size that can be taken is 1.

User Mike Kantor
by
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