A taxi company has been using Brand A tires, and the distribution of kilometers to wear-out has been found to be approximately normal with mean =114,000 and σ = 11,600. Now it tries 12 tires of Brand B and finds a sample mean 117,200. Test at the 5% level of significance to see whether there is a significant difference (positive or negative) in kilometers to wear-out between Brand A and Brand B. Assume the standard deviation is unchanged. Justify your answer.

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A taxi company has been using Brand A tires, and the distribution of kilometers to wear-out has been found to be approximately normal with mean =114,000 and σ = 11,600. Now it tries 12 tires of Brand B and finds a sample mean 117,200. Test at the 5% level of significance to see whether there is a significant difference (positive or negative) in kilometers to wear-out between Brand A and Brand B. Assume the standard deviation is unchanged. Justify your answer.
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