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A small dairy wants to make sure that their butter mill isproducing bricks of butter that do not differ from the labelledweight by too much. The machine produces 30 bricks of butter perminute and runs for 4 hours Monday, Tuesday, and Wednesdaymornings. If the weights of the bricks of butter are deemed to betoo high or too low then that afternoon will be dedicated torecalibrating the machines.

Question 1.

Use a hypothesis test to determine if Monday's sample indicateswe should recalibrate the butter mill.

• a. What are my hypotheses? State them in both words and asequations.
• b. Every hundredth brick is weighed and the weight differencerecorded.
  • Suppose we know the sample values are normallydistributed.
  • On Monday the sample yielded an average of weight differencesof -2.5 g and a sample standard deviation of 10.25 g.
  • Let ?X be a random variable representing the difference betweenthe actual weight of a brick of butter and the desired weight ofthe brick of butter.
  • Write the short hand for the distribution of ?¯X¯ (the samplingdistribution for the sample means).
• c. Draw the sampling distribution.
• d. Complete the hypothesis test using ?=0.03α=0.03.
  • Shade the region for the p-value
  • Compute the p-value.
  • Compare the p-value to the critical value.
• e. Write the conclusion in terms of what the dairy owner shouldplan to do Monday afternoon.