Researchers would like to estimate the mean cholesterol level μ of a variety of monkey. (You know, the kind that Ace Ventura has - a cappuccino monkey?) They would like their estimate to be within 1 milligram per deciliter (mg/dl) of the true value of μ at a 95% confidence level. A previous study involving this variety of monkey suggests that the standard deviation of cholesterol level is about 5 mg/dl.

1. What is the minimum number of monkeys they will need to generate a satisfactory estimate?

Question

Yosef Rowland

Mathematics

21 January, 01:28

Researchers would like to estimate the mean cholesterol level μ of a variety of monkey. (You know, the kind that Ace Ventura has - a cappuccino monkey?) They would like their estimate to be within 1 milligram per deciliter (mg/dl) of the true value of μ at a 95% confidence level. A previous study involving this variety of monkey suggests that the standard deviation of cholesterol level is about 5 mg/dl.

1. What is the minimum number of monkeys they will need to generate a satisfactory estimate?

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Answers (1)

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Immanuel Gibbs · Answer 1

The minimum number of monkeys needed to generate a satisfactory estimate is 96.04 = > 96 approx.

Step-by-step explanation:

We use the idea of margin of error to obtain the minimum sample size (n) require.

By margin of error:

Moe = Z (0.05) * S. E

where S. E = standard deviation (SD) / sqrt (n)

Thus, n = (Z (0.05) * SD) / Moe

=> n = [ (1.96*5) / 1]^2

n = 96.04

n = 96 approx.

We can't use decimal when talking about population or count.