A scientist wishes to estimate the average depth of a river. He wants to be 99% confident that the estimate is accurate within 2 feet. From a previous study, the standard deviation of the depths measured was 4.33 feet. Find the Minimum Sample Size Needed for an Interval Estimate of the POPULATION MEAN

The Minimum Sample Size Needed for an Interval Estimate of the POPULATION MEAN is 32

The given parameters are:

At 99% confidence interval, the z value is 2.575.

So, we start by calculating the margin of error (E) using:

Substitute values for E, z and .

So, we have:

Multiply both sides by

Divide both sides of the equation by 2

Square both sides of the equation

Evaluate the exponent

The smallest integer greater than 31.0792312656 is 32.

So, we have:

Hence, the minimum size is 32

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The minimum sample size needed is 32

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

Find the Minimum Sample Size Needed for an Interval Estimate of the POPULATION MEAN

The minimum sample size needed is n

n is found when M = 2.

We have that

So

Rounding up

The minimum sample size needed is 32

step-by-step explanation:

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