Question

In: Statistics and Probability

Please solve the hypothesis testing problems (#1, and 2) using Minitab as the tool. For each...

Please solve the hypothesis testing problems (#1, and 2) using Minitab as the tool. For each problem, (1) specify the business and statistical hypotheses, (2) specify what the Type I and Type II errors are in this business context, and, the implications of making those errors, (3) include the results from Minitab, (4) draw appropriate conclusions to your statistical hypotheses based on the results, and, finally, (5) present the business conclusions in a short non-statistical summary.

After receiving your bachelor’s degree in personnel management, you were hired by a small but expanding life insurance company. Your first assignment is to develop a more efficient technique for the preliminary screening of applicants for sales positions. Since the firm employs only college graduates, you decide to work with information focusing on their performance during college. A random sample of 25 from the firm’s current sales force is selected and the following information is obtained: Last year’s performance evaluation score College grade point average (GPA) Percent of total college expenses earned by the individual Number of social organizations the individual belonged to

Performance Score

GPA

Expenses Earned

Social Organizations

43

2.1

50

2

47

2.8

20

5

53

2.6

10

3

56

2.7

60

1

57

3.8

0

0

64

2.6

30

2

68

3.2

10

1

68

2.8

30

2

74

2.6

10

2

75

2.9

40

1

77

3.0

30

0

78

3.2

15

1

81

3.4

20

2

83

2.8

40

3

87

2.6

60

5

88

3.1

50

0

89

2.4

80

4

90

3.3

10

2

91

2.9

50

6

92

3.5

40

1

93

3.7

30

2

94

3.1

20

5

95

3.6

70

1

96

3.2

10

4

97

3.4

40

0

(Source: Unknown – 270RL?)

On the basis of the data obtained, what recommendations can you make regarding the preliminary screening of applicants for sales positions?

Solutions

Expert Solution

The regression output is:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.69577329
R Square 0.48410047
Adjusted R Square 0.410400538
Standard Error 12.58804139
Observations 25
ANOVA
df SS MS F Significance F
Regression 3 3122.525491 1040.84183 6.56853341 0.002638877
Residual 21 3327.634509 158.458786
Total 24 6450.16
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -27.28109828 24.07103214 -1.13335806 0.26983772 -77.33954997 22.77735342
GPA 28.75141265 6.907913382 4.16209803 0.00044099 14.38562034 43.11720496
Perc of Exp Earned 0.335066608 0.128293016 2.61172913 0.01629179 0.068266675 0.601866541
No. of Social Orgs 3.211202414 1.593113065 2.01567766 0.05680884 -0.101857572 6.5242624

The regression model is:

y = -27.28 + 28.75*x1 + 0.335*x2 + 3.21*x3

The variable GPA is significant. (p < .05)

The variable Perc of Exp Earned is significant. (p < .05)

The variable No. of Social Orgs is not significant. (p > .05)

Thus, candidates should be screened based on their GPA and Perc of Exp Earned only.


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