Question

In: Statistics and Probability

A small dairy wants to make sure that their butter mill is producing bricks of butter...

A small dairy wants to make sure that their butter mill is producing bricks of butter that do not differ from the labelled weight by too much. The machine produces 30 bricks of butter per minute and runs for 4 hours Monday, Tuesday, and Wednesday mornings. If the weights of the bricks of butter are deemed to be too high or too low then that afternoon will be dedicated to recalibrating the machines.

Question 1.

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

  • a. What are my hypotheses? State them in both words and as equations.
  • b. Every hundredth brick is weighed and the weight difference recorded.
    • Suppose we know the sample values are normally distributed.
    • On Monday the sample yielded an average of weight differences of -2.5 g and a sample standard deviation of 10.25 g.
    • Let ?X be a random variable representing the difference between the actual weight of a brick of butter and the desired weight of the brick of butter.
    • Write the short hand for the distribution of ?¯X¯ (the sampling distribution 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 should plan to do Monday afternoon.

Solutions

Expert Solution

Answer:

Hypotheses:

H0 : the mean difference in the weight is equal to 0
H1 : the mean difference in the weight is not equal to 0

N(-2.5,10.25^2)

We can conclude that the weights of the bricks of butter are not too high or too low hence the machines does not need to be recalibrated


Related Solutions

A small dairy wants to make sure that their butter mill is producing bricks of butter...
A small dairy wants to make sure that their butter mill is producing bricks of butter that do not differ from the labelled weight by too much. The machine produces 30 bricks of butter per minute and runs for 4 hours Monday, Tuesday, and Wednesday mornings. If the weights of the bricks of butter are deemed to be too high or too low then that afternoon will be dedicated to recalibrating the machines. Question 1. Use a hypothesis test to...
What are the key elements of the classical school (Ricardo, Senior, Mill, Malthus)? Make sure to...
What are the key elements of the classical school (Ricardo, Senior, Mill, Malthus)? Make sure to discuss their theory of growth and wages and compare it to more modern views.
Organic Dairy produces an organic butter that is sold by the pound. The production of the...
Organic Dairy produces an organic butter that is sold by the pound. The production of the butter begins in the Churning Department. Units in beginning Work in Process (WIP) inventory 75,000 units Units started during the month (all direct materials, including cream and salt, are added at the beginning of the churning process) 1,800,000 units Units in ending Work in Process (WIP) inventory (50% of the way through the process) 210,000 units Cost information is as follows: WIP - Churning...
WholesomeWholesome Dairy produces an organic butter that is sold by the pound. The production of the...
WholesomeWholesome Dairy produces an organic butter that is sold by the pound. The production of the butter begins in the Churning Department. Data for the Churning Department for JanuaryJanuary follows: Units in beginning Work in Process (WIP) inventory 90,000 units Units started during the month (all direct materials, including cream and salt, are added at the beginning of the churning process) 1,900,000 units Units in ending Work in Process (WIP) inventory (50% of the way through the process) 140,000 units...
E2. Arla is one of the popular dairy products manufacturers. They are producing world popular dairy...
E2. Arla is one of the popular dairy products manufacturers. They are producing world popular dairy products in their company like cheese, yogurt, butter, milk and milk based products. Milk powder is one the fast moving product of this company. Idris is the CEO of that company and he is coordinating various department staffs in that company. Idris having good analytical skills. He is trying to implement the innovative financial management concepts in his organization. Idris quite often calls the...
Suppose a researcher wants to make sure that the probability of committing a Type I error...
Suppose a researcher wants to make sure that the probability of committing a Type I error is less than 5%. How can the researcher control for this? Set the value for a Type II error at 0.05. Set the alpha level at 0.05. Place the rejection region in both tails. Both setting the alpha level at 0.05 and placing the rejection region in both tails.
A textile mill wants to test the strength of the fiber of a certain batch of...
A textile mill wants to test the strength of the fiber of a certain batch of cotton. The Pressley Strength Index measures fiber strength in thousands of pounds of pressure required to break the equivalent of one square inch of fiber. The expected strength level for the population of cotton used by the company is a population mean strength of 90 pounds. The sample of 26 pieces of fiber is drawn. The sample has a mean strength of 85.50 pounds...
Walter's mother, Louise, has lost her home in a flood. Walter wants to make sure that...
Walter's mother, Louise, has lost her home in a flood. Walter wants to make sure that his mother has somewhere to live for her remaining years and wants to allow her to have an ownership interest. Walter owns a plot of land near where his mother's home used to be. Walter wants to offer the land to his mother to own. However, Walter also wants to retain an ownership interest, so that he can build his own retirement home there...
3. One board member wants to make sure that a complete risk analysis, including sensitivity and...
3. One board member wants to make sure that a complete risk analysis, including sensitivity and scenario analyses, is performed before the proposal is sent to the board. a. Perform a sensitivity analysis. b. What management information is provided by the sensitivity analysis?
A small consulting company wants to make the switch to QuickBooks Online. All of their expenses...
A small consulting company wants to make the switch to QuickBooks Online. All of their expenses are paid at the time they are incurred, so there is no need to track bills in the system. There is only one person from the company who requires access to the system. The client wants financial reports such as Profit & Loss and Balance Sheet, A/R, and budget reports. Which of the following QuickBooks products would best suit their requests and requirements? A....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT