question archive A bottled water distributor wants to determine whether the mean amount of water contained in 1- gallon bottles purchased from a nationally known water bottling company is actually 1 gallon

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A bottled water distributor wants to determine whether the mean amount of water contained in 1- gallon bottles purchased from a nationally known water bottling company is actually 1 gallon. You know from the water bottling company specifications that the standard deviation of the amount of water per bottle is 0.02 gallons. You select a random sample of 50 bottles, and the mean amount of water per 1-gallon bottle turns out to be 0.995 gallons in this sample.

- Is there evidence that mean amount is different from 1.0 gallon? (Use alpha = 0.01)
- Given the conclusion, you drew on part A. what type of error are you at risk of making? What is the meaning of this error in this particular problem?
- Compute the p-value for the sample mean.