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loris [4]
3 years ago
11

A limnologist wishes to estimate the mean phosphate content per unit volume of lake water. It is knownfrom studies in previous y

ears that the standard deviation has a fairly stable value ofσ= 4. How manyindependent water samples must the limnologist analyze to be 90% certain that the error of estimation [halfwidth of 90% confidence interval] does not exceed 0.8 milligrams?
Mathematics
1 answer:
telo118 [61]3 years ago
6 0

Answer: 68

Step-by-step explanation:

As per given , we have

Population standard deviation : \sigma=4

Critical value for  90% confidence interval =z_{\alpha/2}=1.645

Margin of error : E= 0.8 milligrams

The formula to find the sample size is given by :-

n=(\dfrac{z_{\alpha/2}\ \sigma}{E})^2

i.e. n=(\dfrac{(1.645)(4)}{0.8})^2=(8.225)^2

=67.650625\approx68

Hence, the limnologist must analyze 68 samples.

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