Ex 12.3.2

1. In order to determine whether or not a cram shcool course improves the scores on

some statistics exam. A sample of 6 students were given the exam before and after taking

the course. The result s are shown below.

Student
1
2
3
4
5
6
Before the Course
83
89
93
77
86
79
After the Course
87
88
91
77
93
83

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(a) What is the standardized test statistic? (to 4 digits)

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(b) Based on the standardized test statistic at10% level of significance,

what is the conclusion?

There is statistical difference in the average scores before and after taking the course.
There is NO statistical difference in the average scores before and after taking the course.

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2. The following data presents the number of computer units sold per day by a sample

of 6 salespersons before and after a bonus plan was implemented.

Salesperson
1
2
3
4
5
6
Before
3
7
6
8
7
9
After
6
5
6
7
8
8


(a)
What is the standardized test statistic?

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(b) Based on the standardized test statistic at 5% level of significance,

what is the conclusion?

There is statistical difference in the average number of computer units sold before and after the bonus plan
There is NO statistical difference in the average number of computer units sold before and after the bonus plan

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3. To determine the effectiveness of a new weight control diet, 10 randomly selected students

students observed the diet for 4 weeks with the results shown below.

Dieter
A
B
C
D
E
F
G
H
I
J
Weight Before
138
151
129
125
168
139
152
140
137
180
Weight After
135
147
132
127
155
131
144
142
137
180

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(a) Find the standard deviation of the differences. (to 3 digits)

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(b) Suppose the 95% confidence interval estimate for the true amount lost on this diet

is [x,y]. What is x? (to 3 digits)

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(c) Based on the 95% confidence interval, what is the conclusion?

There is statistical difference in the average weight before and after the diet
There is NO statistical difference in the average weight before and after the diet

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(d) What is the standardized test statistic? (to 3 digits)

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(e) Based on the standardized test statistic, what is the conclusion?

There is statistical difference in the average weight before and after the diet
There is NO statistical difference in the average weight before and after the diet

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