In standard crash tests of 15 randomly selected Honda miniva

In standard crash tests of 15 randomly selected Honda minivans, their repair costs were found to have a mean of $1786 and a standard deviation of $938.

1. Find a 99% confidence interval for the mean repair costs on Honda minivans in standard crash tests.
2. By finding the endpoints of the CI, what are we predicting about the repair costs of Honda minivans in standard crash tests?
3. Suppose that a histogram of the repair costs in the sample showed a mound-shaped distribtion. Is this important for the valididy of the confidence intercal or not? Why?

Solution

1.

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    1786          
t(alpha/2) = critical t for the confidence interval =    2.976842734          
s = sample standard deviation =    938          
n = sample size =    15          
df = n - 1 =    14          
Thus,              
Margin of Error E =    720.9632047          
Lower bound =    1065.036795          
Upper bound =    2506.963205          
              
Thus, the confidence interval is              
              
(   1065.036795   ,   2506.963205   ) [ANSWER]

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b)

We are 99% confident that the true mean repair cost of Honda Minivans is between $1065.037 and $2506.963. [ANSWER]

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c)

Yes, because we only have 15 samples. So the more mound shaped the original distribution is, the better our confidence interval is.