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Natasha_Volkova [10]
3 years ago
15

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

ost per person for crashes in the Tampa, Florida, area was reported to be $1599. Suppose this average cost was based on a sample of 100 persons who had been involved in car crashes and that the population standard deviation is σ=$500. What the sample size would you recommend if the study required a 98% confidence level and a margin of error of $120 or less?
Mathematics
1 answer:
ivanzaharov [21]3 years ago
8 0

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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