Question

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

                                    Percent of        Number of

Performance                Expenses          Social

Score               GPA    Earned             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

Answer 1

The hypothesis being tested is:

H₀: β₁ = β₂ = β₃ = 0

H₁: At least one β_i ≠ 0

The p-value is 0.0026.

Since the p-value (0.0026) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

The regression model is:

y = -27.2811 + 28.7514*x1 + 0.3351*x2 + 3.2112*x3

The output is:

	R²	0.484
	Adjusted R²	0.410
	R	0.696
	Std. Error	12.588
	n	25
	k	3
	Dep. Var.	Score
ANOVA table
Source	SS	df	MS	F	p-value
Regression	3,122.5255	3	1,040.8418	6.57	.0026
Residual	3,327.6345	21	158.4588
Total	6,450.1600	24
Regression output				confidence interval
variables	coefficients	std. error	t (df=21)	p-value	95% lower	95% upper
Intercept	-27.2811
GPA	28.7514	6.9079	4.162	.0004	14.3856	43.1172
Earned	0.3351	0.1283	2.612	.0163	0.0683	0.6019
Organizations	3.2112	1.5931	2.016	.0568	-0.1019	6.5243