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 σ = $600.
What is the margin of error for a 95% confidence interval (to 2 decimals)?
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To calculate the margin of error for a 95% confidence interval, you can use the following formula:
Margin of Error = Critical value * (Standard deviation / √n)
First, let's find the critical value corresponding to a 95% confidence level. For a normal distribution, the critical value is typically determined using the Z-table or Z-score calculator. Since the sample size is relatively large (n ≥ 30), we can use the Z-distribution.
For a 95% confidence level, the critical value is approximately 1.96.
Next, we need the standard deviation (σ) and the sample size (n):
Standard deviation (σ) = $600
Sample size (n) = 50
Now, we can plug these values into the margin of error formula:
Margin of Error = 1.96 * ($600 / √50)
Calculating this expression:
Margin of Error ≈ 1.96 * ($600 / 7.0711) ≈ $108.03
Therefore, the margin of error for a 95% confidence interval, rounded to 2 decimal places, is approximately $108.03.