Question 1:
A marine biologist has evidence from other studies that the number of fish is declining in certain lakes because of pollution. The biologist decides to compare the fish population of these lakes to the number of fish in the population of lakes of comparable size. A sample of 16 lakes has a mean of 62.000 fish with a standard deviation of 12.000. The population mean is 66,000. Using an alpha level of .05, list (a) the hypotheses, (b) df (c) critical value of t. (d) decision rules, (e) computation, and (f) interpretation of the test.
Question 2:
A company that makes processors for computers uses a .05 significance level to reject any lot of processors that does not run an average of 300 Millions of Instruction Per Second (MIPS). Twenty processors are selected at random to test the quality of six lots. Below are listed the resulting mean number of MIPS for each of the sixlots of processors. Which lots should be rejected as having failed to meet the quality standards? Specify the tcrit you will use for the test as well as the tobs got each lot.
Lot A : x= 502, s = 3.1
Lot B:x= 501.6, s=3.3
Lot C: x = 499,6, s=1.3
Lot D: x = 498,3, s=2.6
Lot E: x =501,4 , s=3.2
Lot F: x= 500.3 s= .6
Question 3:
A team of researchers has developed a test that attempts to predict the use of excessive force that police officers use against suspects. A series of observations on police recruits, psychological profiles, and scores from their police academy training are used to determine a "proneness to use excessive force" score. Ten years later, additional observations, profiles, and data from actual experience are gathered for the same officers that reflects the frequency and extend of excessive force reportedly used. This score is called "force". Suppose these procedures are used with a group of 10 officers who trained at "Academy A" and a separate group of 10 officers who trained at "Academy B". Given the data provided, answer the questions below. (Use α = .05) and ignore the small N used to make computation easier -act as if N 20 in each group except for df). In formulating your answer to each question, list the hypotheses, assumptions, decision rules (including the critical values, directionality of the test, and degrees of freedom if appropriate), computation, and decision.
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Officer from Academy A
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Proneness to Use Excessive Force (x)
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Force (Y)
|
|
A
|
13
|
10
|
|
B
|
16
|
11
|
|
C
|
15
|
11
|
|
D
|
10
|
6
|
|
E
|
19
|
14
|
|
F
|
15
|
9
|
|
G
|
9
|
5
|
|
H
|
15
|
11
|
|
I
|
13
|
8
|
|
J
|
11
|
9
|
|
Officer from Academy B
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Proneness to Use Excessive Force (x)
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Force (Y)
|
|
K
|
12
|
22
|
|
L
|
14
|
20
|
|
M
|
13
|
18
|
|
N
|
9
|
17
|
|
O
|
15
|
23
|
|
P
|
14
|
21
|
|
Q
|
8
|
16
|
|
R
|
11
|
21
|
|
S
|
11
|
18
|
|
T
|
10
|
20
|
a. Test the hypothesis that the officers sampled from Academy A and Academy B do not differ in their proneness to use excessive force score; in their force score.
b. Suppose the date came from 10 police officer partners (Officer A from Academy A is the partner of officer K from Academy B's etc). Again test the hypothesis that officers from Academy A and officers from Academy B do not differ in their proneness to use ecess force scores; in their force scores.
c. Twice you have tested the hypothesis that officers from Academy A and officers from Academy B do not differ with respect to their proneness to use excessive force scores, once using an independent-group test (a) and once using a correlated-group test (b). Suppose, as is quite possible, the correlated-groups analysis gave a significant result (Hº rejected) but the independent -groupsanalysis did not (Hº not rejected). Explain how this would be possible, and explain what advantage correlated-groups research designs might have over independent groups designs (if one has a choice).
d. Test the hypothesis that there is not relationship between the proneness to use excessive force score and the force score for officers trained at Academy A.
e. Test the hypothesis that there is no relationship between the proneness to use excessive force score and the force score for officers trained at Academy A.
f. Test the hypothesis that the two sets of officers do not differ in the magnitude of the relationship assessed in parts d and e.
g. Suppose that the correlations computed in parts d and e were both significant and that part f showed that the two correlations were significantly different from one another. Is this possible? If so, what does it mean?