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Statistics Problems – Inferential Statisitcs On Decision Making

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Question 1:
A program admissions coordinator wanted to know if the math placement test given to a certain cohort of students was an indicator on how well they would perform on their first exam.  She records the scores of their placement test and first exam below.  Is there a correlation between these measures?

Placement
Exam 1

11
49

27
71

7
60

33
85

28
80

23
75

20
61

48
100

35
71

26
81

 
 
 
 
 
 
 
 
Question 2:
The scores below are performance scores for six subjects on Trial 1 and Trial 30 of a test of motor skills.  What test should you pick to measure if there is a relationship between trial 1 and trial 30 for the subjects?  What are the results of the statistical test (write up according to the handbook)?
Trial 1      Trial 30
3             21
6             25
2             20
6             33
5             23
8             34
 
 
 
 
 
Question 3:
Over the past decade, ABC Manufacturing has increased the number of safety inspections per month in hopes to decrease the number accidents on their production line.  Below is a list of how many inspections were conducted in a month and the corresponding number of accidents recorded.  Is there a correlation, and has this leadership decision been effective?

Inspections
Accidents

20
181

24
190

28
167

40
160

60
120

64
124

64
118

68
90

70
94

72
85

 
 
 
 
 
 
Question 4:
The ACT standardized college admission exam was given in three rooms at a local testing site.  A complaint was filed that one of the testing conditions of each room were not the same and caused a difference of scores.  You have been asked to provide a statistical analysis to support or refute the claim.  Determine your hypotheses, run the appropriate test, and provide the appropriate conclusion.
The scores from each of the three rooms were:

Room A
Room B
Room C

21
17
19

16
24
16

14
29
22

17
21
15

12
17
16

19
30
13

34
22
29

14
16
17

26
12
27

36
19
27

 
 
Question 5:
 
A marketing team conducted a survey of 300 people to see if a person’s age affected their brand choice.  People under the age of twenty-five made the following choices: Brand A (25), Brand B (42), Brand C (33).  People over 65 made the following selections: Brand A (20), Brand B (38), Brand C (42).  The group between those ages made these choices: Brand A (44), Brand B(40), Brand C (16).  Form your  hypotheses, run the appropriate test, and provide a conclusion to the marketing team.
 
 
 
 
 
 
 
Question 6:
Five higher education institutions were ranked according to their cost and retention.  The data are listed below.  Which test would you use to determine if there is a correlation?  What are the results (written according to the handbook), and what do they mean?
 

Cost
Retention

1
3

2
2

3
4

4
1

5
5

 
 
 
 
 
 
 
 
 
 
Question 7:
Five higher education institutions were ranked according to their cost and retention.  The data are listed below.  Which test would you use to determine if there is a correlation?  What are the results (written according to the handbook), and what do they mean?
 

Cost
Retention

1
2

2
3

3
5

4
1

5
4

 
 
 
 
 
 
 
 
 
 
Question 8:
You have completed the DSRT 734 course.  It is time to apply your learning.  Respond to each of the following areas:
Design a research question relevant to your specialty area.
Describe what type of data you would gather to answer the research question.
Determine which statistical test would be best to answer your research question.
What would you determine if the results were significant, based on your research question?
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