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Guarantors' Mutual, an insurance company, wants to use a paired-data confidence interval to compare the repair costs of moderately damaged cars at two shops. They

Guarantors' Mutual, an insurance company, wants to use a paired-data confidence interval to compare the repair costs of moderately damaged cars at two shops. They select a random sample of 12 moderately damaged cars, take each car to both shops, and ask how much the necessary repairs will cost. After they receive the cost estimates for each car, they subtract the cost at the first shop from the cost at the second shop. They create a Q-Q plot of the differences and see that the points in the plot roughly form a straight line.

Are the requirements for using the desired confidence interval satisfied? Explain.

Options:

_______

Yes. The distribution of mean differences is normal because the sample size is large.

_______

Yes. The distribution of mean differences is normal because the differences themselves have been determined to be normal.

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No. The distribution of mean differences is not normal because the sample size is not large enough.

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Not necessarily, because the company needs to check that the costs at each shop are normal, not that the differences are normal.

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