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

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?

Answer 1

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.