STASTISTICAL PROBLEMS

Statistical Problems



Statistical Problems

10.51 An experiment has five groups and seven values in

each group.

a. How many degrees of freedom are there in determining

the among-group variation?

Since there are total five groups, therefore, among-group variation will be calculated using following formula.

Among-Group Variation = n-1

N =

5

Among-Group Variation = 5-1

Among-Group Variation = 4

Degrees of freedom for the among-group variation is 4.

10.55 Consider an experiment with four groups, with eight

values in each. For the ANOVA summary table below, fill in

all the missing results:

Mean

Degrees of

Sum of

Square

Source

Freedom

Squares

(Variance)

F

Among

c - 1 = ?

SSA = ?

MSA = 80

FSTAT = ?

groups

Within

n - c = ?

SSW = 560

MSW = ?

groups

Total

n - 1 = ?

SST = ?

Mean

Degrees of

Sum of

Square

Source

Freedom

Squares

(Variance)

F

Among

4

320

80.00

35.71

groups

Within

25

56

2.24

groups

Total

29

376

10.57 The Computer Anxiety Rating Scale (CARS) measures

an individual's level of computer anxiety, on a scale

from 20 (no anxiety) to 100 (highest level of anxiety).

Researchers at Miami University administered CARS to 172

business students. One of the objectives of the study was to

determine whether there are differences in the amount of

computer anxiety experienced by students with different

majors. They found the following:

Degree of

Sum of

Mean of

Source

 

Freedom

Squares

quares

F

Amount major

5

3,172

Within Major

166

21,246

Total

177

24,418

Major

 

n

 

Mean

Marketing

19

44.37

Management

11

43.18

Other

14

42.21

Finance

45

41.8

Accountancy

36

37.36

MIS

47

32.21

a. Complete the ANOVA summary table.

Degree of

Sum of

Mean of

Source

 

Freedom

Squares

quares

F

Amount major

5

3,172

634.40

4.96

Within Major

166

21,246

127.99

Total

177

24,418

b. At the 0.05 level of significance, is there evidence of a

difference in the mean computer anxiety experienced by

different majors?

Using F-value calculator

Df

5

Df

166

Alpha

0.05

F-value tab

2.27

F-value calculated

4.96

Since F-calculated is greater than the F-tabulated critical region; therefore, we reject the null hypothesis.

This shows that there is a significant difference in the mean computer anxiety experienced by different majors.

11.25 Where people turn to for news is different for various

age groups. A study indicated where different age

groups primarily get their news:

 

AGE GROUP

 

 

MEDIA

 

Under 36

 

36 -50

 

50 +

Local TV

107

119

133

National TV

73

102

127

Radio

75

97

109

Local Newapaper

52

79

107

Internet

95

93

76

At the 0.05 level of significance, is there evidence of a significant

relationship between the age group and where people

primarily get their news? If so, explain the relationship.

12.1 Fitting a straight line to a set of data yields the following

prediction line:

 

yi = 2 + 5Xi

a. Interpret the meaning of the Y intercept

, b0

In the above presented equation b0= 2. This shows that when value of x will be zero, Y will bet at level of 2 units.

This shows that minimum consideration of change begins from the level of 2.

b-Interpret the meaning of the slope, b1

In the above presented case, slope (B1) = 5. This shows that for every unit change in the x-value, value of y will increase by 5 units.

Positive change in Y is reported due to unit change in x, since the slope is positive in the equation.

c- Interpret the value of Y if X = 3

When X =3

yi =

2

+

5

Xi

Therefore,

yi =

2

+

5

(3)

yi =

2

+

(15)

yi =

17

References

Hardle, A. (2007), “Applied multivariate statistical analysis”, 2nd edition. Springer Link, pp. 84-245

Ott, L. (2008), An introduction to statistical methods and data analysis. 6th edition. Cengage Learning: pp. ...