Economic Statistics-
Suppose you produce coffee k cups. Last stage of production requires packing cups into boxes. Recently, your provider of machinery designed a new kind of machine that does packing faster and with less damage than the machines he used to supply you with. To test the hypothesis that new machinery is indeed more productive, you receive a sample of ten new machines, then, you take times it takes for each machine to pack 10 boxes. Here are the results for new machines compared to the 10 old ones:
|
New machinery, time in minutes
|
42.1
|
41
|
41.3
|
41.8
|
42.4
|
42.8
|
43.2
|
42.3
|
41.8
|
42.7
|
|
Old machinery, time in minutes
|
42.7
|
43.6
|
43.8
|
43.3
|
42.5
|
43.5
|
43.1
|
41.7
|
44
|
44.1
|
1. The averages of packing time across two samples (1st - new machines, 2nd - old) are:
a) Equal
b) y1- = 42.14, y2- = 43.23
c) y1- = 42.99, y2- = 43.23
d) y1- = 42.14, y2- = 45.16
2. The standard deviation of packing time across two samples (1st - new machines, 2nd - old) are:
a) Equal
b) s1- = 0.145, s2- = 0.243
c) s1- = 0.683, s2- = 0.243
d) s1- = 0.683, s2- = 0.75
3. Are these two samples independent?
a) Yes
b) No
4. The variances seem to be close enough across samples, so you consider equal population variance assumption. What kind of test will you proceed with?
a) Pooled variance t-test
b) Z-test
5. You choose left tail test that difference between the two samples' means is bigger or equal than zero, with α=0.05. What is your pooled estimate of standard deviation?
a) 0.818
b) 0.717
c) 0.919
d) 0.269
6. What is the calculated t-statistic for the test?
a) -4.3
b) -3.4
c) -2.7
d) -7.2
7. What is the rejection region for your hypothesis?
a) t* < -1.734
b) t* < -1.96
c) t* < -1.65
d) t* < 1.734
8. What do you conclude?
a) Fail to reject
b) Reject
9. What does it mean?
a) New machines are more efficient in packing
b) New machines are less efficient in packing
c) There is no statistically significant difference between the new and old machines' performance.
10. Based on your analysis, you decide to replace your machinery with new one. However, your workers have different level of training/skills operating this machinery. You would like to know how the level of your employees' skills impact production. For this you have following data:
|
Worker
|
Grade on the test after training completion
|
Number of boxed coffee cups in thousands per hour
|
|
1
|
1.7
|
3.7
|
|
2
|
1.6
|
3.9
|
|
3
|
2.8
|
6.7
|
|
4
|
5.6
|
9.5
|
|
5
|
1.3
|
3.4
|
|
6
|
2.2
|
5.6
|
|
7
|
1.3
|
3.7
|
|
8
|
1.1
|
2.7
|
|
9
|
3.2
|
5.5
|
|
10
|
1.5
|
2.9
|
|
11
|
5.2
|
10.7
|
|
12
|
4.6
|
7.6
|
|
13
|
5.8
|
11.8
|
|
14
|
3
|
4.1
|
You decide to use OLS to determine the relation between skills of workers and their output.
What are the estimates of the parameters of the regression: of number of boxed coffee cups in thousands (Y) on grade of the worker obtained after training (X)? (in Y=b0+b1X+e b0 and b1 are):
a) 0.965 and 1.67
b) 1.2 and 1.67
c) 0.965 and 0.03
d) 2 and 13.5
11. What is SST for this regression?
a) 203.5
b) 115.7
c) 116.95
d) 11.206
12. What is SSE for this regression?
a) 203.5
b) 115.7
c) 116.95
d) 11.206
13. What is SSR for this regression?
a) 106.93
b) 105.75
c) 116.95
d) 11.206
14. What is R2 for this regression?
a) 0.096
b) 0.904
c) 0.56
d) 205
15. What is standard error for the slope coefficient?
a) 0.5
b) 0.0019
c) 0.157
d) 132
16. You decide to test significance of the slope (b1). What is your calculated t-statistic for the test?
a) 1.2
b) 0.014
c) 10.64
d) 23
17. What do you conclude based on this t-statistic?
a) b1 is statistically significant
b) b1 is not statistically significant
18. In OLS framework the regressors have to be linearly independent:
a) True
b) False
19. In OLS framework E[ε|X]=0
a) True
b) False
20. In simple regression model R2 is equal to the correlation of dependent and independent variables.
a) True
b) False