2. A scientist averages several measurements to estimate the average depth of a river. He wants to be 90% confident that his estimate is accurate to within 0.4 foot. The population standard deviation of the depths measured is σ = 4.5 feet.
A 90% confidence requires ___________ measurements.
A 99% confidence requires _________________measurements.
2)
Solution :
Given that,
Population standard deviation =
= 4.5
Margin of error = E = 0.4
(a)
Z/2
= 1.645
sample size = n = [Z/2*
/ E] 2
n = [1.645 * 4.5 / 0.4]2
n = 343
A 90% confidence requires 343 measurements.
(b)
Z/2
= 2.576
sample size = n = [Z/2*
/ E] 2
n = [2.576 * 4.5 / 0.4]2
n = 840
A 90% confidence requires 840 measurements.
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