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2 years ago

Question 18 of 25

Mathematics

1 answer:

Pani-rosa [81]2 years ago

7 0

Step-by-step explanation:

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The Wall Street Journal reported that automobile crashes cost the United States $162 billion annually (2008 data). The average c

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Answer:

$n=(\frac{2.326(500)}{120})^2 =93.928 \approx 94$

So the answer for this case would be n=94 rounded up to the nearest integer

Step-by-step explanation:

Information given

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma= 500$ represent the population standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =120 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The confidence2 level is 98% or 0.98 then the significance level would be $\alpha=1-0.98=0.02$ and $\alpha/2=0.01$ , the critical value for this case would be $z_{\alpha/2}=2.326$ , replacing into formula (b) we got:

$n=(\frac{2.326(500)}{120})^2 =93.928 \approx 94$

So the answer for this case would be n=94 rounded up to the nearest integer

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