Question: The supervisor of an orange juice bottling company is considering the purchase of a new machine to bottle 16 fluid ounces (473 mL) bottles of 100% pure orange juice and wants an estimate of the difference in the mean filling weights between the new machine and the old machine. The supervisor obtains random samples of bottles of orange juice from each of the machines. Construct a 95% confidence interval for the difference between two population means (assume equal variances). Do the following data indicate that there is a difference in the mean filling weights between the new and the old machines?
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New Machine
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Old Machine
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Sample mean, x¯
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470 mL
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460 mL
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Sample Standard Deviation, s
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5 mL
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7 mL
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Sample size, n
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15
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12
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Need answer in the following format:
1. The problem statement.
2. Your approach.
3. Assumptions.
4. The confidence level.
5. The result and its interpretation.