4. The Clover Milk Company makes milk boxes for school lunches. The company clai

Question

4. The Clover Milk Company makes milk boxes for school lunches. The company claims that each box has an average of 8 ounces of milk, with a standard deviation of 0.2 ounces. Part A: How would you design an experiment to determine if each box really does have 8 ounces of milk on average? (4 points) Part B: You take a sample of 50 milk boxes from Clover Milk Company, and the average amount of milk in each box is 7.6 ounces. Does this mean that the factory is filling each box with less than 8 ounces of milk, on average? Explain. (2 points) Part C: Use Part B and the formula sto find the sample standard deviation of the distribution of sample means. Round to the nearest hundredth. (2 points) Part D: Use Part C to find the 95% confidence interval for the sample and population. Fill in the blanks to explain what the confidence interval means. (2 points) 95% confidence interval ,t 2s- You can expect the sample mean to be between Part E: Use Part D to make a conclusion about the Clover Milk Company's claim that each box has an and ounces 95% of the time average of 8 ounces of milk. Explain your conclusion. (3 points)

Explanation / Answer

A) I would randomly sample more than 30 boxes of Clover milk company of boxes and take their average, and repeat this process multiple time, and then derive a 95% confidence interval to check my hypothesis whether the true mean is 8 litres or not

B) even though the sample has 7.6L on average, nothing can be said about the population as this only a sample and suffers from sampling error, we need to test our hypothesis based on available data before arriving at a conclusion

C) Sample SD = 0.2/sqrt(50) = 0.028 ~0.03

D) 95% CI = 8 +_ 2* 0.03 = (7.94, 8.06)

E) Based on our 95% confidence interval the true mean of the population based on the sample should lie between 7.94, 8.06 L , since 7.6 < 7.94, we can say that Clover Milk Company is not filling each box with an average of 8 ounces of milk

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