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The director of a training program for a large insurance company has the business objective of determining which training method is best for training underwriters

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The director of a training program for a large insurance company has the business objective of determining which training method is best for training underwriters. The three methods to be evaluated are? classroom, online, and courseware app. The 30 trainees are divided into three randomly assigned groups of 10. Before the start of the? training, each trainee is given a proficiency exam that measures mathematics and computer skills. At the end of the? training, all students take the same? end-of-training exam. Let x1=?Proficiency, x2=?Classroom, and x3=Online. Regression analysis was performed to predict the score on the? end-of-training exam and the output is shown? below:

Regression Statistics

Multiple R

0.8926

R? Square   

0.7967

Adj. R Square

0.7733

Standard Error

9.3298

?Observations 

30

ANOVA

DF

SS

MS

F

?P-value

Regresion

3

8869.6375

2956.5458

33.9658

?<0.0001

Residual

26

2263.1625

87.0447

Total

29

11132.8

Coefficients

StdError

t stat

?P-value

Lower? 95%

Upper? 95%

Intercept

?-62.0916

15.9120

?-3.9022

0.0006

?-94.7992

?-29.3839

x1

1.1115            

0.1503

7.3926

?****

?****

?****

x2

?-22.5783

4.1793

?-5.4024

0.0000

?-31.1691

?-13.9876

x3

7.3669

4.1734

1.7652

0.0893

?-1.2116

15.9454

Use the above information to answer questions? a) thru? h)

?a) The correct interpretation of the regression coefficient for the predictor online in the model is

A.

For every additional score in? proficiency, the end of training exam score will increase by 1.1115 points.

B.

An underwriter being trained by the online method is expected to increase the? end-of-training exam score by 7.3669 points more than the one who is trained by the courseware app method or the classroom method .

C.

For every 1 unit increase in online? training, the end of training exam score will increase by 7.3669 points.

D.

While holding the proficiency score? constant, an underwriter being trained by the online method is expected to increase the? end-of-training exam score by 7.3669 points more than the one who is trained by the courseware app method.

?b) The appropriate null and alternate hypotheses for the test of the significance of the model? are:

A.

H0:μ1=μ2=μ3=0   Vs  HA: Not all μi are equal to 0? (i=1,2,3)

B.

H0:β1=β2=β3=0   Vs  HA: Not all βi are equal to 0  ?(i=1,2,3)

C.

H0:μ1=μ2=μ3 Vs  HA: Not all μi are equal to each other ? (i=1,2,3)

D.

H0:β1=β2=β3   Vs  HA: Not all βi are equal to each other   ?(i=1,2,3)

?c) For the test of the model? significance, the value of the test statistic is? _____.

A.

0.7967

B.

3.9022

C.

9.3298

D.

33.9658

?d) What is the best conclusion for the test of the significance of the? model?

A.

Reject H0.

B.

There is insufficient evidence to conlcude that at least one of the proficiency and the training methods of the trainee is significant in predicting the score of the? end-of-training exam.

C.

There is sufficient evidence to conclude that at least one of the proficiency and the training methods of the trainee is significant in predicting the score of the? end-of-training exam.

D.

?Don't reject H0.

?e) Which of the following expression is the reduced equation for predicting the score of the? end-of-training exam for one who trained with online training method.

A.

 

EndExamScore=−62.0916+1.1115Proficiency

B.

 

EndExamScore=−54.7247+1.1115Proficiency

C.

 

EndExamScore=−62.0916+1.1115?Proficiency-22.5783Classroom

D.

 

EndExamScore=−84.6746+1.1115Proficiency

?f) What is the appropriate null and alternate hypotheses to test the significance of the predictor proficieny in the? model?

A.

H0:β1≠0   Vs  HA: β1=0

B.

H0:b1≠0   Vs  HA: b1=0

C.

H0:β1=β2=β3=0   Vs  HA:Not all βi=0

D.

H0:β1=0   Vs  HA: β1≠0

?g) What is the best conclusion  for the test of the significance of the predictor proficiency in the? model?

A.

There is insufficient evidence to conclude that proficiency is statistically significant in predicting the? end-of-training exam score.

B.

Reject H0.

C.

?Don't reject H0.

D.

There is sufficient evidence to conclude that proficiency is statistically significant in predicting the? end-of-training exam score.

?h) The? 95% confidence interval for β1 is closest to

A.

?(0.9138,1.3092)

B.

?(0.8550,1.3679)

C.

?(0.8025,1.4204)

D.

?(0.7138,1.5205)