Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume Total Cost (units) ($) 400 3,900 450 4,900 550 5,400 600 6,000 700 6,400 750 6.900 This data was used to develop an estimated regression equation, ý = 1,121.33 +7.76x, relating production volume and cost for a particular manufacturing operation. Use a = 0.05 to test whether the production volume is significantly related to the total cost. (Use the F test.) State the null and alternative hypotheses. OH: B₂ 20 H₂: B₂ <0 OH: B₁₂ #0 OH: B₁ = 0 H₂: Po #0 OH: B₁ = 0 H₂B₁ = = 0 OH ₁: B₁ = 0 H₁₂: A₁ = 0 Set up the ANOVA table. (Round your p-value to three decimal places and all other values to two decimal places.) Source Sum Degrees of Freedom F Mean Square p-value of Variation of Squares Regression Error Total Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value= What is your conclusion? O Reject H. We conclude that the relationship between production volume and total cost is significant. O Do not reject H. We conclude that the relationship between production volume and total cost is significant. O Reject H. We cannot conclude that the relationship between production volume and total cost is significant. O Do not reject H. We cannot conclude that the relationship between production volume and total cost is significant. H₂: Bo = 0
Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume Total Cost (units) ($) 400 3,900 450 4,900 550 5,400 600 6,000 700 6,400 750 6.900 This data was used to develop an estimated regression equation, ý = 1,121.33 +7.76x, 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. (Use the F test.) State the null and alternative hypotheses. OH: B₂ 20 H₂: B₂ <0 OH: B₁₂ #0 OH: B₁ = 0 H₂: Po #0 OH: B₁ = 0 H₂B₁ = = 0 OH ₁: B₁ = 0 H₁₂: A₁ = 0 Set up the ANOVA table. (Round your p-value to three decimal places and all other values to two decimal places.) Source Sum Degrees of Freedom F Mean Square p-value of Variation of Squares Regression Error Total Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value= What is your conclusion? O Reject H. We conclude that the relationship between production volume and total cost is significant. O Do not reject H. We conclude that the relationship between production volume and total cost is significant. O Reject H. We cannot conclude that the relationship between production volume and total cost is significant. O Do not reject H. We cannot conclude that the relationship between production volume and total cost is significant. H₂: Bo = 0
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
100%
![**Sample Data for Production Volumes and Total Costs**
Consider the following sample of production volumes and total cost data for a manufacturing operation:
| Production Volume (units) | Total Cost (\$) |
|---------------------------|-----------------|
| 400 | 3,900 |
| 450 | 4,500 |
| 550 | 5,400 |
| 600 | 6,000 |
| 700 | 6,600 |
| 750 | 6,900 |
This data was used to develop an estimated regression equation, \( \hat{y} = 1,121.33 + 7.76x \), relating production volume and cost for a particular manufacturing operation. Use \( \alpha = 0.05 \) to test whether the production volume is significantly related to the total cost. (Use the **F** test.)
### Steps in Hypothesis Testing
1. **State the null and alternative hypotheses.**
\[
\begin{aligned}
& \mathrm{H}_{0}: \beta_{1} \geq 0 \\
& \mathrm{H}_{a}: \beta_{1} < 0
\end{aligned}
\]
\[
\begin{aligned}
& \mathrm{H}_{0}: \beta_{1} = 0 \\
& \mathrm{H}_{a}: \beta_{1} \neq 0
\end{aligned}
\]
\[
\begin{aligned}
& \mathrm{H}_{0}: \beta_{1} \leq 0 \\
& \mathrm{H}_{a}: \beta_{1} > 0
\end{aligned}
\]
2. **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 | | | | | |
3. **Find the value of the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4959d4f7-c515-4b84-8a14-00389cef5562%2F6f1be893-84a4-4326-92d2-fa639976f69e%2F2wipec5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:
**Sample Data for Production Volumes and Total Costs**
Consider the following sample of production volumes and total cost data for a manufacturing operation:
| Production Volume (units) | Total Cost (\$) |
|---------------------------|-----------------|
| 400 | 3,900 |
| 450 | 4,500 |
| 550 | 5,400 |
| 600 | 6,000 |
| 700 | 6,600 |
| 750 | 6,900 |
This data was used to develop an estimated regression equation, \( \hat{y} = 1,121.33 + 7.76x \), relating production volume and cost for a particular manufacturing operation. Use \( \alpha = 0.05 \) to test whether the production volume is significantly related to the total cost. (Use the **F** test.)
### Steps in Hypothesis Testing
1. **State the null and alternative hypotheses.**
\[
\begin{aligned}
& \mathrm{H}_{0}: \beta_{1} \geq 0 \\
& \mathrm{H}_{a}: \beta_{1} < 0
\end{aligned}
\]
\[
\begin{aligned}
& \mathrm{H}_{0}: \beta_{1} = 0 \\
& \mathrm{H}_{a}: \beta_{1} \neq 0
\end{aligned}
\]
\[
\begin{aligned}
& \mathrm{H}_{0}: \beta_{1} \leq 0 \\
& \mathrm{H}_{a}: \beta_{1} > 0
\end{aligned}
\]
2. **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 | | | | | |
3. **Find the value of the
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman