A snack food producer produces bags of peanuts labeled as containing 3 ounces. T

Question

A snack food producer produces bags of peanuts labeled as containing 3 ounces. The actual weight of peanuts packaged in individual bags is Normally distributed with mean and standard deviation = 0.2 ounces. As part of quality control, n bags are selected randomly and their contents are weighed. The hypotheses of interest are H0: = 3 ounces, Ha : 3 ounces. If the inspector samples n = 5000 bags and observes a sample mean weight of = 3.01 ounces, the P-value is 0.00041. Then . . .

the inspector will conclude that there is strong evidence that the mean weight of peanut bags is very different from 3 ounces.

the inspector will commit a Type I error by concluding that the mean weight of peanut bags is different from 3 ounces.

the P-value is close to 0 simply because we took such a large sample. After all, it's clear that the true mean weight for all peanut bags is not exactly 3 ounces. So while we may have evidence that the mean weight differs from 3 ounces, there's no evidence that it is far from 3 ounces.

we need a larger sample to determine that the mean weight for all peanut bags is very different from 3 ounces.

Explanation / Answer

Note that 3.01 is not really far from 3.00 ounces. We of course know that the weight is not exactly 3.00 ounces, so this is not practically significant. Hence,

Hence,

OPTION C: the P-value is close to 0 simply because we took such a large sample. After all, it's clear that the true mean weight for all peanut bags is not exactly 3 ounces. So while we may have evidence that the mean weight differs from 3 ounces, there's no evidence that it is far from 3 ounces. [ANSWER, C]

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