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. A bear biologist is planning a survey of female Kodiak grizzly bears to estimate the percent that are pregnant. Examining a bear for pregnancy is risky business (duh) and the researcher doesn't want to survey too many or too few bears (just right). How many bears must be surveyed to be 99% confident that the measured pregnancy rate (proportion pregnant) is within no more than 5 percentage points of the true value? Based on an initial survey of 16 bears she expects a pregnancy rate of 32%.

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Answer:

 Hence the value of n should be 580.

Step-by-step explanation:

Consider the provided information.

It is given that e = 0.05

p = 32% = 0.32

The confidence interval is 99%

for 99% CI critical Z = 2.580

We can calculate the sample size  by using the formula.

[tex]n = p (1-p)(\frac{z_{\frac{\alpha}{2}}}{e})^2[/tex]

Substitute the respective values

[tex]n =0.32(1-0.32)(\frac{2.58}{0.05})^2[/tex]

[tex]n =0.2176(2662.56)[/tex]

[tex]n =579.37[/tex]

Hence the value of n should be 580.

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