Solution Found!
Solved: In their book Introduction to Time Series Analysis
Chapter 6, Problem 123SE(choose chapter or problem)
In their book Introduction to Time Series Analysis and Forecasting (Wiley, 2008), Montgomery, Jennings, and Kulahci presented the data on the drowning rate for children between one and four years old per 100,000 of population in Arizona from 1970 to 2004. The data are:
19.9, 16.1, 19.5, 19.8, 21.3, 15.0, 15.5, 16.4, 18.2, 15.3, 15.6, 19.5, 14.0, 13.1, 10.5, 11.5, 12.9, 8.4, 9.2, 11.9, 5.8, 8.5, 7.1, 7.9, 8.0, 9.9, 8.5, 9.1, 9.7, 6.2, 7.2, 8.7, 5.8, 5.7, and 5.2.
(a) Perform an appropriate graphical analysis of the data.
(b) Calculate and interpret the appropriate numerical summaries.
(c) Notice that the rate appears to decrease dramatically starting about 1990. Discuss some potential reasons explaining why this could have happened.
(d) If there has been a real change in the drowning rate beginning about 1990, what impact does this have on the summary statistics that you calculated in part (b)?
Questions & Answers
QUESTION:
In their book Introduction to Time Series Analysis and Forecasting (Wiley, 2008), Montgomery, Jennings, and Kulahci presented the data on the drowning rate for children between one and four years old per 100,000 of population in Arizona from 1970 to 2004. The data are:
19.9, 16.1, 19.5, 19.8, 21.3, 15.0, 15.5, 16.4, 18.2, 15.3, 15.6, 19.5, 14.0, 13.1, 10.5, 11.5, 12.9, 8.4, 9.2, 11.9, 5.8, 8.5, 7.1, 7.9, 8.0, 9.9, 8.5, 9.1, 9.7, 6.2, 7.2, 8.7, 5.8, 5.7, and 5.2.
(a) Perform an appropriate graphical analysis of the data.
(b) Calculate and interpret the appropriate numerical summaries.
(c) Notice that the rate appears to decrease dramatically starting about 1990. Discuss some potential reasons explaining why this could have happened.
(d) If there has been a real change in the drowning rate beginning about 1990, what impact does this have on the summary statistics that you calculated in part (b)?
ANSWER:Answer
Step 1 of 4
(a)
The data on the drowning rate for children between one and four years old per of the population in Arizona from
The data are:
19.9 16.1 19.5 19.8 21.3 15.0 15.5 16.4 18.2 15.3 15.6 19.5 14.0 13.1 10.5 11.5 12.9 8.4 9.2 11.9 5.8 8.5 7.1 7.9 8.0 9.9 8.5 9.1 9.7 6.2 7.2 8.7 5.8 5.7 5.2
We are asked to perform an appropriate graphical analysis of the data.
Step to create the Stem-and-leaf display in Minitab:
- On the opening of Minitab, you will get session handler and worksheet like Excel worksheet.
- Enter the data into the worksheet (in this case drowning rate).
- After entering the data go to the menu called Graph in menu panel.
- In the Graph menu select option Stem-and-leaf, you will get one window of Stem-and-leaf.
- Under the Stem-and-leaf window, Select the drowning rate variable as Graph variables.
- After everything entered correctly, press ok and you will get the Stem-and-leaf Display of your data.
Figure 1: Stem-and-leaf diagram of Drowning rate
Step to create the time-series plot in Minitab:
- On the opening of Minitab, you will get session handler and worksheet like Excel worksheet.
- Enter the data into the worksheet (in this case drowning rate).
- After entering the data go to the menu called Graph in menu panel.
- In the Graph menu select option Time Series plot, you will get one window of Time Series plot.
- Under the Time Series plot window, Select the drowning rate variable as Graph variables.
- After everything entered correctly, press ok and you will get the Time Series Plot of your data.
Figure 2: Time Series Plot of Drowning rate