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const2013 [10]
3 years ago
5

The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident th

at the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?
Mathematics
1 answer:
Aleks04 [339]3 years ago
6 0

Answer:

The minimum sample size that can be taken is of 14 dogs.

Step-by-step explanation:

The formula for calculating the minimum sample size to estimate a population mean is given by:

n=\frac{z^{2}\sigma^{2}}{e^{2}}

The <u>first step</u> is obtaining the values we're going to use to replace in the formula.

Since we want to be 95% confident, 1-\alpha=0.95 \Rightarrow \alpha=0.05.

Therefore we look for the critical value z_{\alpha/2}=1.96.

Then we calculate the variance:

\sigma = 3.7 \Rightarrow \sigma^{2}=13.69

And we have that:

e=2 \Rightarrow e^{2}=4

<u>Now</u> we replace in the formula with the values we've just obtained:

n=\frac{1.96^{2}*13.69}{4}=13.1479\approx 14

Therefore the minimum sample size that can be taken to guarantee that the sample mean is within 2 inches of the population mean is of 14 dogs.

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