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

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.

 

  1. Is there evidence that mean amount is different from 1.0 gallon? (Use alpha = 0.01)
  2. 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?
  3. Compute the p-value for the sample mean.

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