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How many women must be randomly selected to estimate the…

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How many women must...

How many women must be randomly selected to estimate the mean weight of women in one age group. We want​ 90% confidence that the sample mean is within
2.52.5
lb of the population​ mean, and the population standard deviation is known to be
2929
lb.

Submitted: 8 months ago.Category: Calculus and Above
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11/14/2017
Tutor: Ryan, Engineer replied 8 months ago
Ryan
Ryan, Engineer
Category: Calculus and Above
Satisfied Customers: 9,184
Experience: B.S. in Civil Engineering
Verified

Hi,

Thank you for using the site. I'll be happy to help you with this problem.

The calculation for the required minimum sample size is:

n = (z * σ / E)^2

For a 90% confidence level, use z = 1.645.

Then, with E = 2.5 and σ = 29, the required minimum sample size would be:

n = (1.645 * 29 / 2.5)^2 = 364.1

However, since the value of n is a minimum, but the sample size must also be an integer, the calculated value must be rounded up to the next whole number: 365.

Solution: n = 365

If this value is marked as incorrect, it may be that your course wants you to use a value z with only 2 digits after the decimal point. That is, z = 1.65. That change would make the minimum sample size 366 instead of 365.

Please feel free to ask if you have any questions about this solution.

Thanks,

Ryan

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