Question

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ANOVA df SS MS F Significance F Regression 4 1917837 479459.2 7730.595 1.18E-24 Residual 15 930.3149...

ANOVA
df SS MS F Significance F
Regression 4 1917837 479459.2 7730.595 1.18E-24
Residual 15 930.3149 62.02099
Total 19 1918767
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 36.35267 17.99446 2.020215 0.061592 -2.00161 74.70694 -2.00161 74.70694
PAPER 1.15115 0.101065 11.3902 8.79E-09 0.935735 1.366565 0.935735 1.366565
MACHINE 1.710568 0.384347 4.450582 0.000467 0.891352 2.529785 0.891352 2.529785
OVERHEAD 0.63468 0.473494 1.340418 0.200059 -0.37455 1.643908 -0.37455 1.643908
LABOR -0.03908 0.031298 -1.24858 0.230956 -0.10579 0.027632 -0.10579 0.027632

(a) In the cost accounting literature, the sample regression coefficient corresponding to xk is regarded as an estimate of the true marginal cost of output associated with the variable xk. Find a point estimate of the true marginal cost associated with total machine hours per month. (Enter your answer to three decimal places.)

Also, find a 95% confidence interval estimate of the true marginal cost associated with total machine hours. (Round your answers to three decimal places.)

(b) Test the hypothesis that the true marginal cost of output associated with total production of paper is $1,000. (Hint: Realize that this is analogous to testing the regression coefficient for total production of paper is 1.0.) Use a 10% level of significance.

State the hypotheses to be tested.

a.H0: β1 ≠ 1.0
Ha: β1 = 1.0

b.H0: β1 = 1.0
Ha: β1 ≠ 1.0    

c.H0: β2 ≠ 1.0
Ha: β2 = 1.0

d.H0: β0 = 1.0
Ha: β0 ≠ 1.0

e.H0: β2 = 1.0
Ha: β2 ≠ 1.0

(c)State the decision rule.

a.Reject H0 if p < 0.10.
Do not reject H0 if p ≥ 0.10.

b.Reject H0 if p > 0.05.
Do not reject H0 if p ≤ 0.05.    

c.Reject H0 if p > 0.10.
Do not reject H0 if p ≤ 0.10.

d.Reject H0 if p < 0.05.
Do not reject H0 if p ≥ 0.05.

(d)State your decision.

a.Reject the null hypothesis. The true marginal cost of output associated with total production of paper is not $1,000.

b.Reject the null hypothesis. The true marginal cost of output associated with total production of paper may be $1,000.    

c.Do not reject the null hypothesis. The true marginal cost of output associated with total production of paper may be $1,000.

d.Do not reject the null hypothesis. The true marginal cost of output associated with total production of paper is not $1,000.

Solutions

Expert Solution

ANOVA

df

SS

MS

F

Significance F

Regression

4

1917837

479459.2

7730.595

1.18E-24

Residual

15

930.3149

62.02099

Total

19

1918767

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

36.35267

17.99446

2.020215

0.061592

-2.00161

74.70694

-2.00161

74.70694

PAPER

1.15115

0.101065

11.3902

8.79E-09

0.935735

1.366565

0.935735

1.366565

MACHINE

1.710568

0.384347

4.450582

0.000467

0.891352

2.529785

0.891352

2.529785

OVERHEAD

0.63468

0.473494

1.340418

0.200059

-0.37455

1.643908

-0.37455

1.643908

LABOR

-0.03908

0.031298

-1.24858

0.230956

-0.10579

0.027632

-0.10579

0.027632

(a) In the cost accounting literature, the sample regression coefficient corresponding to xk is regarded as an estimate of the true marginal cost of output associated with the variable xk. Find a point estimate of the true marginal cost associated with total machine hours per month. (Enter your answer to three decimal places.)

Also, find a 95% confidence interval estimate of the true marginal cost associated with total machine hours. (Round your answers to three decimal places.)

Regression coefficient for Machine = 1.711

95% confidence interval = (0.891, 2.530)

(b) Test the hypothesis that the true marginal cost of output associated with total production of paper is $1,000. (Hint: Realize that this is analogous to testing the regression coefficient for total production of paper is 1.0.) Use a 10% level of significance.

State the hypotheses to be tested.

b.H0: β1 = 1.0
Ha: β1 ≠ 1.0    

(c)State the decision rule.

a.Reject H0 if p < 0.10.
Do not reject H0 if p ≥ 0.10.

(d)State your decision.

a.Reject the null hypothesis. The true marginal cost of output associated with total production of paper is not $1,000.

(Note: calculated t= 11.3902, P= 8.79E-09 which is < 0.10 level of significance)

milcah answered 5 months ago
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