Question Week 4:
Consider the following scenario: An industrial seller of grass seeds packages its product in 50-pound bags. A customer has recently filed a complained alleging that the bags are underfilled. A production manager randomly samples a batch and measures the following weights:
Weight, (lbs)
45.6 49.5
47.7 46.7
47.6 48.8
50.5 48.6
50.2 51.5
46.9 50.2
47.8 49.9
49.3 49.8
53.1 49.3
49.5 50.1
To determine whether the bags are indeed being underfilled by the machinery, the manager must conduct a test of mean with a significance level α = 0.05.
1. State appropriate null (Ho) and alternative (H1) hypotheses. What is the critical value if we work with a significant level α = 0.05?
2. What is the decision rule?
3. What is Test statistic? Calculate the test statistic.
Question Week 5:
Advertisement ($’000) Sales ($’000)
1068 4489
1026 5611
767 3290
885 4113
1156 4883
1146 5425
892 4414
938 5506
769 3346
677 3673
1184 6542
1009 5088
1. Construct a scatter plot with this data. Do you observe a relationship between both variables?
2. What is the slope? What does the slope tell us?Is the slope significant?
3. What is the value of the regression coefficient,r? What is the value of the coefficient of determination, r^2? What does r^2 tell us?
Questions Week 6:
1. Time series decomposition seeks to separate the time series (Y) into 4 components: trend (T), cycle (C), seasonal (S), and irregular (I). What is the difference between these components?
2. The model can be additive or multiplicative.When we do use an additive model? When do we use a multiplicative model?
The following list gives the gross federal debt(in millions of dollars) for the U.S. every 5 years from 1945 to 2000:
Year Gross Federal Debt ($millions)
1945 260,123
1950 256,853
1955 274,366
1960 290,525
1965 322,318
1970 380,921
1975 541,925
1980 909,050
1985 1,817,521
1990 3,206,564
1995 4,921,005
2000 5,686,338
3. Construct a scatter plot with this data. Do you observe a trend? If so, what type of trend do you observe?