A snack food producer produces bags of peanuts labelled as containing 30 grams. The actual weight of peanuts packaged in individual bags is Normally distributed with mean μ and standard deviation σ = 0.2 grams. As part of quality control, n bags are selected randomly and their contents are weighed. The hypotheses of interest are H0: μ = 30 grams, Ha: μ ≠ 30 grams.
If the inspector samples n = 5000 bags and observes a sample mean weight of 30.01 grams, the P-value is close to 0 (you don't need to verify this—it's true). Which of the following statements is true?

Question

A snack food producer produces bags of peanuts labelled as containing 30 grams. The actual weight of peanuts packaged in individual bags is Normally distributed with mean μ and standard deviation σ = 0.2 grams.   As part of quality control, n bags are selected randomly and their contents are weighed. The hypotheses of interest are H0: μ = 30 grams, Ha: μ ≠ 30 grams. 
 If the inspector samples n = 5000 bags and observes a sample mean weight of 30.01 grams, the P-value is close to 0 (you don't need to verify this—it's true). Which of the following statements is true?

Accepted Answer

The P-value is close to 0 because we took such a large sample. After all, it's clear that the true mean weight for all peanut bags is not exactly 30 grams. So while we may have evidence that the mean weight differs from 30 grams, the real difference may be negligible.

✅

Answer

The inspector will be making a mistake by concluding that the mean weight of peanut bags is different from 30 grams.

Answer

The inspector will conclude that there is strong evidence that the mean weight of peanut bags is very different from 30 grams.

Answer

we need a larger sample to determine that the mean weight for all peanut bags is very different from 30 grams.

Crowdly

A snack food producer produces bags of peanuts labelled as containing 30 grams....

Want instant access to all verified answers on learning.monash.edu?