Question

In: Statistics and Probability

Carlson Mining, Inc. has 12 large pumps that pump water from the mines it operates. Management...

Carlson Mining, Inc. has 12 large pumps that pump water from the mines it operates.
Management has been concerned lately about the amount of money required to
repair malfunctioning pumps. These costs are sums over and above the amounts
spent for routine maintenance. When asked what factors they thought might affect
the mean monthly repair costs, employees suggested the age of the pumps and the
number of hours of operation. The following information was collected.
Choose the relevant Summary Output to answer the questions. Note that the
mean monthly repair costs are in dollars, so when questions ask about repair
costs, make sure that your answers reflect that.
Mean Weekly Hours of Operation over Past Year Age of Pump at First of Year (months) Mean Monthly Repair Costs over Past Year
28 80 $1,049
26 48 $1,095
15 27 $882
12 2 $447
16 13 $715
21 55 $542
13 30 $415
21 35 $454
16 36 $495
12 13 $370
18 28 $448
18 49 $509
What is the estimate for the mean monthly repair costs if the pump is 40 months old
at the first of the year and the pump is typically in operation for 20 hours per week?
Is there a significant relationship overall between the mean monthly repair costs and
the age of the pumps and the mean weekly hours of operations the .10 level of
significance? Yes   No Defend your answer.

Solutions

Expert Solution

Excel:

Data --> Data analysis --> Regression

ANOVA
df SS MS F Significance F
Regression 2 363822.3883 181911.2 4.689688 0.040234891
Residual 9 349106.5283 38789.61
Total 11 712928.9167
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -87.70037103 261.5249413 -0.33534 0.745051 -679.3108903 503.9101
Mean Weekly Hours of Operation over Past Year 45.09732343 21.8704701 2.062019 0.069253 -4.377117167 94.57176
Age of Pump at First of Year (months) -3.047157232 5.329493207 -0.57175 0.581485 -15.10330846 9.008994

estimate for the mean monthly repair costs = -87.7004+(45.0973*20)-(3.047157*40) =692.35932

Is there a significant relationship overall between the mean monthly repair costs and
the age of the pumps and the mean weekly hours of operations the .10 level of
significance? Yes   No Defend your answer.

Ans : Yes, because significance F = 0.040234891 <0.10


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