1. The following table represents frequency counts of types of transportation used by the publishing and computer hardware industries. Analyse the data to determine whether the transportation mode used to ship goods independent of type of industry? (α = 0.01)
|
|
Transportation mode
|
|
Industry
|
Air
|
Train
|
Truck
|
|
Publishing
|
32
|
12
|
41
|
|
Computer Hardware
|
5
|
6
|
24
|
2. A consulting firm presents a one-week training on reputation management to various clients. The training seminar is sometimes presented to high-level managers, sometimes to mid-level managers, and sometimes to low-level managers. Suppose the data below are some randomly selected scores from different levels of managers who attended the training.
|
High (x1)
|
Medium (x2)
|
Low (x3)
|
|
7
|
9
|
6
|
|
7
|
9
|
5
|
|
7
|
10
|
5
|
|
9
|
8
|
8
|
|
8
|
8
|
4
|
|
|
10
|
7
|
|
|
8
|
|
|
X-1 = 7.6
|
x-2 = 8.857
x- = 7.5
|
x-3 = 5.833
|
a. Given that the SST (Sum of Squares Total) is 48.5, set out the analysis of variance (ANOVA) table.
b. Stating your null and alternative hypotheses, test if there is a significant difference between the exam scores according to manager level (α = 0.05).
3. A manager believes that business trip costs to New York increased significantly between 2004 and 2014. To test this belief, the manger samples 51 business trips from the company's record for 2004 and finds that the sample average was 190$ per day with a population standard deviation of 18.5$. The manager selects a second random samples of 47 business trips from the company's records for 2014 and finds that the sample average was 198$ per day with a population standard deviation of 15.6$.
a. Can the manager conclude that the average trip expenses increased significantly between 2004 and 2014 (α = 0.01)?
b. Would your decision change if the significance level was 5%?
c. Assume that the auditor did not know the population standard deviations of the trip expenses to New York in 2004 and 2014. Moreover, he/she obtained the sample standard deviations for 2004 and 2014 as 20$ and 19$ (variances can be assumed equal), respectively. At 5% significance level, can the auditor conclude that an average trip expense has increased since 2004?
4. A professor wants to compare the students' midterm and final exam results. For a random sample 10 students, the scores obtained are as follows.
|
Midterm (x)
|
Final (y)
|
|
50
|
66
|
|
40
|
57
|
|
45
|
87
|
|
48
|
45
|
|
53
|
61
|
|
41
|
49
|
|
77
|
88
|
|
9195
|
91
|
|
668
|
63
|
|
4123
|
40
|
Σx = 540, Σy = 647, Σxy = 37522, Σx2 = 33026, Σy2 = 44915
a. Find the sample correlation between the midterm and final examination results.
b. Test at 1% level if there is a significant correlation between midterm and final examination results of the students.