The Wall Street Journal reported that automobile crashes cost the United States $162 billion annually (The Wall Street Journal, March 5, 2008). The average cost per person for crashes in the Tampa, Florida, area was reported to be $1599. Suppose this average cost was based on a sample of 50 persons who had been involved in car crashes and that the population standard deviation is ó = $600. What is the margin of error for a 95% confidence interval? What would you recommend if the study required a margin of error of $150 or less?

Question

The Wall Street Journal reported that automobile crashes cost the United States $162 billion annually (The Wall Street Journal, March 5, 2008). The average cost per person for crashes in the Tampa, Florida, area was reported to be $1599. Suppose this average cost was based on a sample of 50 persons who had been involved in car crashes and that the population standard deviation is ó = $600. What is the margin of error for a 95% confidence interval? What would you recommend if the study required a margin of error of $150 or less?

Answer 1

Mean of error = Za/2* σ/√n

= 1.96* 600/√50
= $166.31
For the next part you have to change the 95% confidence level to something lower but at 90% it is at 139.16

I'm not sure what margin of error is correct but it's somewhere between 90%-95% !!

Answer 2

To find the margin of error for a 95% confidence interval, you can use the formula:

Margin of Error = Critical Value * (Standard Deviation / √n)

In this case, the critical value is based on a 95% confidence level, which corresponds to a z-score of approximately 1.96. The standard deviation (σ) is given as $600, and the sample size (n) is 50.

So, let's calculate the margin of error:

Margin of Error = 1.96 * ($600 / √50)
= 1.96 * ($84.85)
≈ $166.34

Therefore, the margin of error for a 95% confidence interval is approximately $166.34.

If the study required a margin of error of $150 or less, it would mean that the desired level of precision is stricter. In this case, you would need to decrease the margin of error by reducing the sample size or increasing the standard deviation.

To decrease the margin of error, you could either collect a larger sample size or reduce the variability in the population. Collecting a larger sample size would ensure a smaller standard error, and therefore a smaller margin of error. Alternatively, if you could reduce the standard deviation (σ) significantly, the margin of error would also decrease.

It's important to note that any changes made to the sample size or standard deviation should be done with caution to maintain the study's integrity and avoid biases. Additionally, practical considerations, such as time and resources, may limit the options for reducing the margin of error.