1. A study conducted at ANU finds that a typical office worker spends an average of 13 minutes per hour on non work related activities such as face book. On a trial basis, management sets up a new enclosed work station for a randomly selected group of 12 workers and finds that the average number of minutes lost per hour is 11.3 with a standard deviation of 3.7. At the 5% level of significance, can we conclude that the work station represents a significant change?
2. Five hundred graduates were cross classified by socio-economic group and the presence or absence of a certain skill gap. The results were as shown below.
|
|
Socio- economic group
|
|
Skill Gap
|
Upper
|
Upper middle
|
Lower middle
|
Lower
|
|
Present
|
8
|
24
|
32
|
27
|
|
Absent
|
42
|
121
|
138
|
108
|
Are the data compatible with the hypothesis that skill gap is unrelated to socio-economic status of the graduates at α = 0.10?
3. The following are the sales revenues (in millions of shillings) generated by four salesmen situated in four different regions of a country.
|
Region A
|
Region B
|
Region C
|
Region D
|
|
13
|
12
|
18
|
8
|
|
9
|
11
|
12
|
10
|
|
12
|
9
|
16
|
12
|
|
16
|
14
|
6
|
8
|
|
15
|
4
|
8
|
7
|
Perform a one way analysis of variance at α = 0.05 to confirm whether salesman location influences the amount of revenues generated.
4. The responses from a group of religious leaders on an item of Likert's attitude scale were recorded as follows:
|
|
Strongly disagree
|
disagree
|
Undecided
|
agree
|
Strongly agree
|
Total
|
|
Christian
|
12
|
18
|
4
|
8
|
12
|
54
|
|
Muslim
|
48
|
22
|
10
|
8
|
10
|
98
|
|
Hindu
|
10
|
4
|
12
|
10
|
12
|
48
|
|
Total
|
70
|
44
|
26
|
26
|
34
|
200
|
At 1% level of significance, do the data indicate that the opinions expressed are independent of the religion professed by the respondents?
5. The following data were collected from two separate groups of 144 men and 175 women on an attitude scale.
|
|
Mean
|
SD
|
|
MEN
|
19.7
|
6.08
|
|
WOMEN
|
21.0
|
4.89
|
a. Test the significance of the difference between the mean of the two groups at the 0.05 level of significance.
b. In your own words, what does the result of the experiment say?