Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume (units) Total Cost ($) 400 4,000 450 4,900 550 5,300 600 5,900 700 6,400 750 7,000 This data was used to develop an estimated regression equation, ŷ = 1,121.33 + 7.76x, relating production volume and cost for a particular manufacturing operation. Use ? = 0.05 to test whether the production volume is significantly related to the total cost. (Use the F test.) State the null and alternative hypotheses. -H0: ?1 ≠ 0 Ha: ?1 = 0 -H0: ?1 ≥ 0 Ha: ?1 < 0 -H0: ?0 ≠ 0 Ha: ?0 = 0 -H0: ?1 = 0 Ha: ?1 ≠ 0 -H0: ?0 = 0 Ha: ?0 ≠ 0 Set up the ANOVA table. (Round your p-value to three decimal places and all other values to two decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Regression ? ? ? ? ? Error ? ? ? Total ? ? Find the value of the test statistic. (Round your answer to two decimal places.) Test statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? What is your conclusion? -Reject H0. We cannot conclude that the relationship between production volume and total cost is significant. -Do not reject H0. We cannot conclude that the relationship between production volume and total cost is significant. - Do not reject H0. We conclude that the relationship between production volume and total cost is significant. -Reject H0. We conclude that the relationship between production volume and total cost is significant.
Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume (units) Total Cost ($) 400 4,000 450 4,900 550 5,300 600 5,900 700 6,400 750 7,000 This data was used to develop an estimated regression equation, ŷ = 1,121.33 + 7.76x, relating production volume and cost for a particular manufacturing operation. Use ? = 0.05 to test whether the production volume is significantly related to the total cost. (Use the F test.) State the null and alternative hypotheses. -H0: ?1 ≠ 0 Ha: ?1 = 0 -H0: ?1 ≥ 0 Ha: ?1 < 0 -H0: ?0 ≠ 0 Ha: ?0 = 0 -H0: ?1 = 0 Ha: ?1 ≠ 0 -H0: ?0 = 0 Ha: ?0 ≠ 0 Set up the ANOVA table. (Round your p-value to three decimal places and all other values to two decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Regression ? ? ? ? ? Error ? ? ? Total ? ? Find the value of the test statistic. (Round your answer to two decimal places.) Test statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? What is your conclusion? -Reject H0. We cannot conclude that the relationship between production volume and total cost is significant. -Do not reject H0. We cannot conclude that the relationship between production volume and total cost is significant. - Do not reject H0. We conclude that the relationship between production volume and total cost is significant. -Reject H0. We conclude that the relationship between production volume and total cost is significant.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Consider the following sample of production volumes and total cost data for a manufacturing operation.
| Production Volume (units) |
Total Cost ($) |
|---|---|
| 400 | 4,000 |
| 450 | 4,900 |
| 550 | 5,300 |
| 600 | 5,900 |
| 700 | 6,400 |
| 750 | 7,000 |
This data was used to develop an estimated regression equation,
ŷ = 1,121.33 + 7.76x,
relating production volume and cost for a particular manufacturing operation. Use
? = 0.05
to test whether the production volume is significantly related to the total cost. (Use the F test.)State the null and alternative hypotheses.
-H0: ?1 ≠ 0
Ha: ?1 = 0
Ha: ?1 = 0
-H0: ?1 ≥ 0
Ha: ?1 < 0
Ha: ?1 < 0
-H0: ?0 ≠ 0
Ha: ?0 = 0
Ha: ?0 = 0
-H0: ?1 = 0
Ha: ?1 ≠ 0
Ha: ?1 ≠ 0
-H0: ?0 = 0
Ha: ?0 ≠ 0
Ha: ?0 ≠ 0
Set up the ANOVA table. (Round your p-value to three decimal places and all other values to two decimal places.)
| Source of Variation |
Sum of Squares |
Degrees of Freedom |
Mean Square |
F | p-value |
|---|---|---|---|---|---|
| Regression | ? | ? | ? | ? | ? |
| Error | ? | ? | ? | ||
| Total | ? | ? |
Find the value of the test statistic. (Round your answer to two decimal places.)
Test statistic=??
Find the p-value. (Round your answer to three decimal places.)
p-value = ??
What is your conclusion?
-Reject H0. We cannot conclude that the relationship between production volume and total cost is significant.
-Do not reject H0. We cannot conclude that the relationship between production volume and total cost is significant.
- Do not reject H0. We conclude that the relationship between production volume and total cost is significant.
-Reject H0. We conclude that the relationship between production volume and total cost is significant.
Expert Solution
Step 1
Sol:-
The null and alternative hypotheses for this problem are:
H0: β1 = 0 (production volume is not significantly related to total cost)
Ha: β1 ≠ 0 (production volume is significantly related to total cost)
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