At the end of their first year of teaching, 11 teachers were jointly ranked by two school administrators to reflect their relative degree of teaching competence. Unknown to the administrators, some teachers had been supported by a mentor throughout their first year, while the remainder had not. The researchers conducting this study wished to know whether or not mentoring improved teaching competence.
|
Participants
|
Ranking
|
Received Mentoring
|
|
A
|
4
|
Yes
|
|
B
|
9
|
No
|
|
C
|
7
|
No
|
|
D
|
6
|
Yes
|
|
E
|
5
|
No
|
|
F
|
3
|
Yes
|
|
G
|
2
|
No
|
|
H
|
10
|
No
|
|
I
|
11
|
No
|
|
J
|
1
|
Yes
|
|
K
|
8
|
Yes
|
a. What statistical test will you use and why?
Normal since the P value is (I will use T- test since there is one independent variable with two levels and a dependant variable
b. What do you conclude?
c. There is no statistically significant difference since the p value is 0.553. It means the mentoring doesn't have effect on teachers' degree of competence
2. Dr. Shirley Fitter believes that self esteem is an important factor influencing academic success. She also believes that regular aerobic exercise is related to increased self esteem. Dr. Fitter randomly selects 25 graduate students from a pool of 250 at a local university. Each student is asked to keep a record of the number of hours of he/she participates in aerobic exercise over a 4-week period. From these records, Dr. Fitter calculates the average number of hours that each participant participates in aerobic exercise per week. Dr. Fitter also identifies each participant's level of self-esteem using the Rosenberg Self-Esteem Scale. (NOTE: The higher the score on this scale, the greater the degree of self esteem.). Dr. Fitter wishes to know whether there is a relationship between the amount of aerobic exercise and self esteem.
|
Participants
|
Hours/Week of Aerobic Exercise
|
Self-Esteem Score
|
|
1
|
10
|
25
|
|
2
|
33
|
37
|
|
3
|
9
|
12
|
|
4
|
14
|
32
|
|
5
|
3
|
22
|
|
6
|
12
|
31
|
|
7
|
7
|
30
|
|
8
|
15
|
30
|
|
9
|
3
|
15
|
|
10
|
21
|
34
|
|
11
|
2
|
18
|
|
12
|
20
|
37
|
|
13
|
4
|
19
|
|
14
|
8
|
33
|
|
15
|
0
|
10
|
|
16
|
17
|
35
|
|
17
|
25
|
39
|
|
18
|
2
|
13
|
|
19
|
18
|
35
|
|
20
|
3
|
15
|
|
21
|
27
|
35
|
|
22
|
4
|
17
|
|
23
|
8
|
20
|
|
24
|
10
|
22
|
|
25
|
0
|
14
|
a. What statistical test will you use and why?
b. What do you conclude?
3. Mr. Hood, a high school physical education teacher, wishes to teach archery to his Grade 12 students. He has three shape options for the target from which to choose. Mr. Hood decides that he would like to choose the option that will provide the best possibility of success for his students. He, therefore, randomly chooses 10 Grade 12 students from his classes and asks each student to shoot 30 arrows at each of the differently shaped targets. Given the data provided in the table below, will Mr. Hood choose one particular target shape to use in his archery class?
|
|
Target Shape
|
|
Participants
|
Circle
|
Square
|
Triangle
|
|
1
|
10
|
12
|
14
|
|
2
|
18
|
10
|
16
|
|
3
|
20
|
15
|
16
|
|
4
|
12
|
10
|
12
|
|
5
|
19
|
20
|
21
|
|
6
|
25
|
22
|
20
|
|
7
|
18
|
16
|
17
|
|
8
|
22
|
18
|
18
|
|
9
|
17
|
14
|
12
|
|
10
|
23
|
20
|
18
|
a. What statistical test will you use and why?
b. What do you conclude?
4. A team of reading researchers is interested in studying lateralization of cortical functioning in word recognition. They randomly select 10 participants and ask them to look at a central spot on a computer screen and press a key on recognition of a word that may appear on either side of the spot. A total of 100 words are shown, half of which are on the left side of the dot and half of which are on the right side. An average reaction time (in milliseconds) for each visual field (right vs. left) is calculated for each participant. The researchers hypothesize that words presented in the right visual field will be more quickly recognized than those in the left visual field. Do the data in the table below suggest that this hypothesis is correct?
|
Participants
|
Left Field
|
Right Field
|
|
1
|
323
|
304
|
|
2
|
512
|
493
|
|
3
|
502
|
491
|
|
4
|
385
|
365
|
|
5
|
453
|
426
|
|
6
|
343
|
320
|
|
7
|
543
|
523
|
|
8
|
440
|
442
|
|
9
|
682
|
580
|
|
10
|
590
|
564
|
a. What statistical test will you use and why?
b. What do you conclude?
5. Two new drugs have been approved for treating attention deficit hyperactivity disorder (ADHD) in children. Researchers are interested in comparing the length of time that each of these drugs is effective in reducing ADHD behaviours. A sample of 12 children diagnosed with ADHD has been randomly selected and each child has been observed over a period of 24 hours after receiving Drug A. After a week's time interval, each child is observed over a period of 24 hours after receiving Drug B. The data show the length of time (in hours) after the drug has been administered before symptoms of ADHD recur. Do the data suggest that one drug lasts longer than the other?
|
Participants
|
Drug A
|
Drug B
|
|
1
|
2.0
|
3.5
|
|
2
|
3.6
|
5.7
|
|
3
|
2.6
|
2.9
|
|
4
|
2.6
|
2.4
|
|
5
|
7.3
|
9.9
|
|
6
|
3.4
|
3.3
|
|
7
|
14.9
|
16.7
|
|
8
|
6.6
|
6.0
|
|
9
|
2.3
|
3.8
|
|
10
|
2.0
|
4.0
|
|
11
|
6.8
|
9.1
|
|
12
|
8.5
|
20.9
|
a. What statistical test will you use and why?
b. What do you conclude?