MGMT2263
Worksheet #5
1) In a small private school, class sizes are kept to under 10 students. Three classes were chosen to see if there was any significant difference in the grades of the students. Seven students were sampled from each class. These were the results:
|
Class 1 |
Class 2 |
Class 3 |
|
98 |
82 |
64 |
|
86 |
92 |
74 |
|
76 |
90 |
76 |
|
66 |
99 |
86 |
|
30 |
74 |
67 |
|
76 |
61 |
80 |
|
85 |
59 |
82 |
Is there any significant difference in the grades of the three classes? Do not assume the data is normally distributed. Test at 5%. (chi-square = 0.3915; conclude no significant difference among classes)
2) In a study for a museum, people were asked to rate six different exhibits on a scale from 1 to 10, 10 being the best. Suppose that for a sample of 10 people, these were the results:
|
|
A |
B |
C |
D |
E |
F |
|
Person #1 |
8 |
3 |
2 |
3 |
3 |
7 |
|
Person #2 |
5 |
5 |
5 |
1 |
9 |
1 |
|
Person #3 |
8 |
10 |
8 |
7 |
10 |
8 |
|
Person #4 |
4 |
5 |
5 |
3 |
6 |
2 |
|
Person #5 |
10 |
9 |
9 |
7 |
10 |
6 |
|
Person #6 |
10 |
9 |
2 |
5 |
6 |
4 |
|
Person #7 |
5 |
6 |
8 |
8 |
2 |
3 |
|
Person #8 |
8 |
6 |
6 |
8 |
7 |
9 |
|
Person #9 |
10 |
10 |
10 |
10 |
10 |
10 |
|
Person
#10 |
6 |
6 |
5 |
7 |
8 |
6 |
Is there any significant difference in how people rank the 6 exhibits? Test at 5%. (chi-square = 6.5143; conclude no significant difference among exhibits)
You are given the following data of shipping distance and the time it takes for a shipment to travel that distance by courier.
|
Distance in km |
825 |
215 |
1070 |
550 |
480 |
920 |
1350 |
325 |
670 |
1215 |
|
Time in days |
3.5 |
1 |
4 |
2 |
1 |
3 |
4.5 |
1.5 |
3 |
5 |
3) Construct a model in which the shipping time depends on the distance. State what the model is. (time = 0.1181 + 0.0036*distance)
4) What percentage of the variation in shipping time is explained by the model? (90.05%)
5) Test the hypothesis that the model is significant at the 5% level of significance. (F = 72.3959; conclude model is significant)
6) Construct a 95% confidence interval of the slope coefficient. If this interval were used to test the hypothesis in question 5, why would the same conclusion be reached? (0.0026 < B1 < 0.0046; hypothesized coefficient of zero is not in the interval)
7) In theory, the residuals are normally distributed with a mean of zero and a common variance. What is the estimate of that variance? (0.2304)
8) Test the hypothesis that there is a significant direct relationship between the variables at a 5% level of significance. (t = 8.51; conclude there is a significant direct relationship)
9) If the distance is 500 km, how many days should you expect the shipping time to be? Round to 2 decimals. (1.91 days)
10) If the distance is 500 km, what is the range of the average shipping time for 95% of the time? (1.48 to 2.34 days)
11) For a particular shipment that travels 500 km, what is the range of the shipping time for 95% of the time? (0.72 to 3.1 days)
Suppose you are given the following information:
X = size of home (in thousands of square feet)
Y = home price (in thousands of dollars)
|
size |
1.82 |
1.59 |
1.57 |
1.81 |
2.01 |
1.57 |
1.87 |
1.82 |
1.59 |
1.95 |
|
price |
173.1 |
160 |
164.6 |
183.5 |
194.8 |
166 |
178.7 |
181.5 |
160.5 |
196.5 |
12) Construct a model in which the home price depends on the home size (price = 43.4702 + 75.2556*size)
13) What percentage of the variation in price is explained by the model? (88.52%)
14) Test the hypothesis that the model is significant at the 5% level of significance. (F = 61.6842; conclude model is significant)
15) Construct a 95% confidence interval of the slope coefficient. If this interval were used to test the hypothesis in question 14, why would the same conclusion be reached? (53.1597 < B1 < 97.3515; hypothesized coefficient of zero is not in the interval)
16) If a home has 1500 square feet, what would you expect the price to be? Round to the nearest hundred. ($156,400)
17) If the square footage is 1500 square feet, what is the range of the average home price for 95% of the time? Round to the nearest hundred. ($149,600 to $163,100)
18) If a particular home with 1500 square feet is put up for sale, what is the range of the selling price of this home for 95% of the time? Round to the nearest hundred. ($143,400 to $169,300)