This data was used to develop an estimated regression equation, ý = 1,405.33 + 7.44x, relating production volume and cost for a particular manufacturing operation. Use a = 0.05 to test whether the production volume is significantly related to the total cost. ( %3D F test.) State the null and alternative hypotheses.
This data was used to develop an estimated regression equation, ý = 1,405.33 + 7.44x, relating production volume and cost for a particular manufacturing operation. Use a = 0.05 to test whether the production volume is significantly related to the total cost. ( %3D F test.) State the null and alternative hypotheses.
Chapter4: Linear Functions
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Transcribed Image Text:Consider the following sample of production volumes and total cost data for a manufacturing operation.
Production Volume
Total Cost
(units)
($)
400
4,100
450
5,100
550
5,400
600
6,000
700
6,500
750
7,000
This data was used to develop an estimated regression equation, ŷ = 1,405.33 + 7.44x, relating production volume and cost for a
particular manufacturing operation. Use a = 0.05 to test whether the production volume is significantly related to the total cost. (U
F test.)
%3D
State the null and alternative hypotheses.
O Ho: B1 + 0
H3: B1 = 0
O Ho: Po + 0
H3: Po = 0
O Ho: B1 = 0
H3: B1 # 0
O Ho: B1 2 0
Ha: B1 < 0
%3D
O Ho: Po = 0
H: Bo # 0
Set up the ANOVA table. (Round your p-value to three decim olaces and all other values to two decimal places.)
Degrees
of Freedom
Source
Sum
Mean
F
p-value
of Variation
of Squares
Square
Regression
5.18
1
51.89
86.87
0.0007
Error
23.89
4
59.73
Total
75.78
5
Find the value of the test statistic. (Round your answer to two decimal places.)
9.32
Find the p-value. (Round your answer to three decimal places.)
p-value = 0.0007
What is your conclusion?
O Do not reject Ho. We conclude that the relationship between production volume and total cost is significant.
O Reject Ho. We conclude that the relationship between production volume and total cost is significant.
O Do not reject Ho. We cannot conclude that the relationship between production volume and total cost is significant.
Reject Ho. We cannot conclude that the relationship between production volume and total cost is significant.
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