A machine that packages 500-gram boxes of sugar-coated wheat cereal

Exercise 1:

A machine that packages 500-gram boxes of sugar-coated wheat cereal is being studied. The weights for a random sample of 100 boxes of cereal packaged by this machine are given in the attached file.

The quality control analyst wants to estimate the actual amount of sugar-coated wheat cereal contained in 500-gram boxes produced. It is known from the manufacturing specifications that the standard deviation of the amount of wheat cereal is equal to 9.4 grams.

1.1 Set up a 99% confidence interval estimate of the population mean wheat cereal weight.

1.2 On the basis of your results, do you think that the quality control analyst has a right to complain to the production manager? Why?

1.3 Does the population amount of sugar-coated wheat cereal per box have to be normally distributed here? Explain.

1.4 Explain why an observed value of 509.4grams for an individual box is not unusual, even though it is outside the confidence interval you calculated.

1.5 Suppose that you used a 95% confidence interval estimate. What would be your answers to 1.1 and 1.2?

Exercise 2:

John Halikias, plant manager at HOU Vacuum Products, located in Patras, Ahaia, applies statistical thinking in his workplace. As a major supplier to automobile manufacturers, HOU wants to be sure that the leak rate (in cubic centimetres per second) of transmission oil coolers (TOCs) meets the established specification limits. A random sample of 50 TOCs is tested, and the leak rates are recorded in the attached file.

2.1 Estimate with 95% confidence the mean leak rate for this particular product.

2.2 Chyundai Motors, one of the largest customers of HOU Vacuum Products, requires that the leak rate of transmission oil coolers should not exceed the value of 0.05 cubic centimetres per second.

2.2.1 State the null and the alternative Hypotheses

2.2.2 Test the hypothesis at α = 5%

2.2.3 On the basis of your results, are Chyundai Motors requirements satisfied?

Exercise 3:

In a recent study of university libraries, undergraduate students were asked whether they thought that the libraries had an adequate collection of books. The survey results are stored in the attached data file.

3.1 Find an unbiased point estimate of the proportion of students who think that the collection is adequate (code as 1 = yes, 2 = no).

3.2. Find a 95% confidence interval for the proportion of students who think that the library collections are adequate.

3.3 According to the Ministry of Education statistics, the total number of students reaches 500,000. Set up a 95% confidence interval estimate of the population number of students who are not satisfied with the libraries books collection.

Exercise 4:

Do the data of Exercise 4 support the hypothesis that the proportion of students who think that the library collections are adequate is the same for all years of studies?

4.1 State the null and the alternative Hypotheses

4.2 Test the hypothesis at α = 1%

4.3 What is your conclusion?

Exercise 5:

MBA60 Inc. is a small, but growing, producer of hot and ready-to-eat breakfast cereals. Two machines are used for packaging 510-gram (18-ounce) boxes of sugar-coated wheat cereal. Estimate the difference in the mean weights of boxes of this type of cereal packaged by the two machines. Use a 95% confidence level and the data in the attached file. Explain your findings.

Note: Use the Z statistic with standard error of (Mean1-Mean2) = (s₁²/n₁ + s₂²/n₂)^1/2