Homework Help is Here – Start Your Trial Now!
Math
Statistics
How long it takes paint to dry can have an impact on the production capacity of a business. An auto body & paint business invested in a paint-drying robot to speed up its process. An interesting question is, "Do all paint-drying robots have the same drying time? To test this, suppose we sample fifteen drying times for each four different brands of paint-drying robots. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Suppose the following data were obtained. At the a- 0.05 level of significance, test to see whether the mean drying time is the same for each type of robot. State the null and alternative hypotheses. H H, H O Hai At least two of the population means are equal. H At least two of the population means are different. H: Not all the population means are equal. O H: Not all the population means are equal. Develop a side-by-side box and whisker plot that shows the distribution of drying time for the four types of robots. 150 140 120 110 100 Robot 1 Robot 2 Robot 3 Robot 4 170 160 150 130 120 110 Robot 1 Robot 2 Robot 3 Robot 4

How long it takes paint to dry can have an impact on the production capacity of a business. An auto body & paint business invested in a paint-drying robot to speed up its process. An interesting question is, "Do all paint-drying robots have the same drying time? To test this, suppose we sample fifteen drying times for each four different brands of paint-drying robots. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Suppose the following data were obtained. At the a- 0.05 level of significance, test to see whether the mean drying time is the same for each type of robot. State the null and alternative hypotheses. H H, H O Hai At least two of the population means are equal. H At least two of the population means are different. H: Not all the population means are equal. O H: Not all the population means are equal. Develop a side-by-side box and whisker plot that shows the distribution of drying time for the four types of robots. 150 140 120 110 100 Robot 1 Robot 2 Robot 3 Robot 4 170 160 150 130 120 110 Robot 1 Robot 2 Robot 3 Robot 4

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
100%
Robot Drying Time
Robot 2 146
Robot 2 146
Robot 2 133
Robot 3 141
Robot 1 131
Robot 4 149
Robot 3 136
Robot 4 140
Robot 4 132
Robot 2 132
Robot 3 119
Robot 1 137
Robot 2 142
Robot 1 137
Robot 2 147
Robot 3 143
Robot 4 141
Robot 1 128
Robot 2 135
Robot 4 150
Robot 3 137
Robot 1 124
Robot 4 152
Robot 2 144
Robot 1 137
Robot 3 133
Robot 1 139
Robot 2 137
Robot 1 141
Robot 2 128
Robot 4 153
Robot 1 121
Robot 2 130
Robot 4 135
Robot 1 135
Robot 4 142
Robot 4 146
Robot 1 140
Robot 3 139
Robot 4 151
Robot 3 138
Robot 4 161
Robot 2 134
Robot 3 137
Robot 4 139
Robot 1 128
Robot 1 139
Robot 4 134
Robot 3 139
Robot 1 130
Robot 4 135
Robot 3 137
Robot 2 143
Robot 1 128
Robot 3 131
Robot 2 146
Robot 3 135
Robot 3 136
Robot 3 139
Robot 2 142
### Box Plots of Drying Times for Robots #### Graph Explanation The image contains two box plots illustrating the drying times for four different robots, labeled Robot 1, Robot 2, Robot 3, and Robot 4. - **Upper Box Plot:** - **Y-axis (Drying Time):** Ranges from 110 to 170. - **Observations:** - Robot 1 has a median drying time around 140 with minimal spread. - Robot 2 shows less variability with a slightly lower median. - Robot 3 has a higher median and larger variability. - Robot 4 has the most variability and a slightly lower median than Robot 3. - **Lower Box Plot:** - **Y-axis (Drying Time):** Ranges from 90 to 150. - **Observations:** - Similarly, Robot 1 shows a consistent drying time around 120. - Robot 2's drying time is again closely clustered. - Robot 3 shows less variability than earlier, with consistent middle-range drying times. - Robot 4 maintains a higher variability with some lower drying times observed. #### Statistical Analysis - **Task:** - Find the value of the test statistic and the p-value. - **Conclusion Options:** - You are asked to decide if there is enough evidence to reject the null hypothesis \( H_0 \) that states the mean drying times for all four robots are equal. - **Selected Conclusion:** - The third option is chosen, indicating that you reject \( H_0 \). This suggests there is sufficient evidence to conclude that the mean drying times for the four robots are not all equal. This analysis helps in understanding the performance differences among the robots in terms of their drying times.
Transcribed Image Text:### Box Plots of Drying Times for Robots #### Graph Explanation The image contains two box plots illustrating the drying times for four different robots, labeled Robot 1, Robot 2, Robot 3, and Robot 4. - **Upper Box Plot:** - **Y-axis (Drying Time):** Ranges from 110 to 170. - **Observations:** - Robot 1 has a median drying time around 140 with minimal spread. - Robot 2 shows less variability with a slightly lower median. - Robot 3 has a higher median and larger variability. - Robot 4 has the most variability and a slightly lower median than Robot 3. - **Lower Box Plot:** - **Y-axis (Drying Time):** Ranges from 90 to 150. - **Observations:** - Similarly, Robot 1 shows a consistent drying time around 120. - Robot 2's drying time is again closely clustered. - Robot 3 shows less variability than earlier, with consistent middle-range drying times. - Robot 4 maintains a higher variability with some lower drying times observed. #### Statistical Analysis - **Task:** - Find the value of the test statistic and the p-value. - **Conclusion Options:** - You are asked to decide if there is enough evidence to reject the null hypothesis \( H_0 \) that states the mean drying times for all four robots are equal. - **Selected Conclusion:** - The third option is chosen, indicating that you reject \( H_0 \). This suggests there is sufficient evidence to conclude that the mean drying times for the four robots are not all equal. This analysis helps in understanding the performance differences among the robots in terms of their drying times.
**Analysis of Drying Times in Paint-Drying Robots** Understanding how long paint takes to dry can significantly impact the productivity of an auto body and paint business. To enhance efficiency, a company invested in a paint-drying robot. A key question arose: "Do all paint-drying robots have the same drying time?" To explore this, fifteen drying times were sampled for each of four different kinds of paint-drying robots. The time, measured in minutes, was noted from when the paint dried enough for a second coat to be applied. The collected data is analyzed to determine if there's a significant difference in the drying times across different robots. ### Hypothesis Testing To test the differences in drying times, we set up the null and alternative hypotheses: 1. \( H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4 \) - (Null Hypothesis: All population means are equal.) 2. \( H_a: \) Not all population means are equal. - (Alternative Hypothesis: At least one population mean is different.) The null hypothesis assumes there's no significant difference in drying times among the four robot types, while the alternative hypothesis suggests otherwise. ### Box Plot Analysis A side-by-side box and whisker plot is developed to visually represent the distribution of drying times for the four robots. - **Robot 1**: - Drying time mostly ranges from 70 to 110 minutes. - Median around 90 minutes. - Few outliers on the lower end. - **Robot 2**: - Wider range from 70 to 130 minutes. - Median slightly above 100 minutes. - Outliers and data variability are more pronounced. - **Robot 3**: - Ranges from about 90 to 150 minutes. - Higher median around 120 minutes. - Displays the most substantial interquartile range, indicating high variability. - **Robot 4**: - Range similar to Robot 1, around 75 to 120 minutes. - Median approximately 95 minutes. - Some spread observed with outliers. ### Conclusion The box plots provide a clear comparison of drying times between the four robot types, allowing businesses to infer which robot offers more consistent and fast drying times. Statistical tests can further confirm any significant difference suggested by these visual observations.
Transcribed Image Text:**Analysis of Drying Times in Paint-Drying Robots** Understanding how long paint takes to dry can significantly impact the productivity of an auto body and paint business. To enhance efficiency, a company invested in a paint-drying robot. A key question arose: "Do all paint-drying robots have the same drying time?" To explore this, fifteen drying times were sampled for each of four different kinds of paint-drying robots. The time, measured in minutes, was noted from when the paint dried enough for a second coat to be applied. The collected data is analyzed to determine if there's a significant difference in the drying times across different robots. ### Hypothesis Testing To test the differences in drying times, we set up the null and alternative hypotheses: 1. \( H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4 \) - (Null Hypothesis: All population means are equal.) 2. \( H_a: \) Not all population means are equal. - (Alternative Hypothesis: At least one population mean is different.) The null hypothesis assumes there's no significant difference in drying times among the four robot types, while the alternative hypothesis suggests otherwise. ### Box Plot Analysis A side-by-side box and whisker plot is developed to visually represent the distribution of drying times for the four robots. - **Robot 1**: - Drying time mostly ranges from 70 to 110 minutes. - Median around 90 minutes. - Few outliers on the lower end. - **Robot 2**: - Wider range from 70 to 130 minutes. - Median slightly above 100 minutes. - Outliers and data variability are more pronounced. - **Robot 3**: - Ranges from about 90 to 150 minutes. - Higher median around 120 minutes. - Displays the most substantial interquartile range, indicating high variability. - **Robot 4**: - Range similar to Robot 1, around 75 to 120 minutes. - Median approximately 95 minutes. - Some spread observed with outliers. ### Conclusion The box plots provide a clear comparison of drying times between the four robot types, allowing businesses to infer which robot offers more consistent and fast drying times. Statistical tests can further confirm any significant difference suggested by these visual observations.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS