Question

The report "Wireless Substitution: Early Release of Estimates from the National Health Interview Survey" (Center for Disease Control, 2009 ) gave the following estimates of the percentage of homes in the United States that had only wireless phone service at 6-month intervals from June 2005 to December 2008 . \begin{tabular}{lr} & Percent with Only \\ Date & Wireless Phone Service \\ \hline June 2005 & 7.3 \\ December 2005 & 8.4 \\ June 2006 & 10.5 \\ December 2006 & 12.8 \\ June 2007 & 13.6 \\ December 2007 & 15.8 \\ June 2008 & 17.5 \\ December 2008 & 20.2 \\ \hline \end{tabular} Construct a time-series plot for these data and describe the trend in the percent of homes with only wireless phone service over time. Has the percent increased at a fairly steady rate?

Short answer

The percentage of homes switching to only wireless phone service seems to be increasing steadily over the given period, as indicated by the positive trend in our time-series plot.

Step-by-step solution

Understanding the data

The data given in the exercise is a collection of time-series data which lists the percentage of homes in the US with only wireless phone service at six-month intervals from June 2005 to December 2008.

Constructing the time-series plot

This is done by plotting the dates on the x-axis and the corresponding percentage on the y-axis. Each coordinate will be formed by the (date, percentage) pair. Then connect each point in the order of the date.

Examining the trend

After plotting, the trend of the data can be seen by observing the plotted graph. Here, the trend is seen by observing how the percentage increases over time. To determine if the increase is at a steady rate, you should observe if the line connecting the points is relatively straight or if it shows irregular fluctuation.

Interpret the graph

Describe the trend observed in the time-series plot. An increase in the percentage can indicate more homes are switching to only wireless phone service. If the line observed is relatively straight with gradual increase, then the increase can be said to be at a steady rate.

Key concepts

Wireless Substitution

Wireless substitution refers to the shift from traditional landline telephones to wireless phone services in homes. This change occurs as technological advancements make wireless communication more accessible and efficient. The data from 2005 to 2008 shows the gradual increase in households switching to only wireless service. Sitting at 7.3% in June 2005 and reaching 20.2% by December 2008, it reflects a significant shift in how people communicate. Several factors drive this trend:

• Cost-effectiveness: Wireless phones eliminate the need for managing two separate phone bills, making them a more economical option.
• Mobility: Wireless phones offer users the convenience of making calls from anywhere.
• Technology advancements: Innovations in mobile technology have provided better service coverage and reliability.

These factors contribute to why an increasing percentage of households have made the switch away from landlines.

Trend Analysis

Trend analysis involves studying data to identify patterns or trends over time. In this context, it helps to understand how the percentage of homes with only wireless service evolves. To analyze trends, you can follow these steps:

• Collect data at consistent intervals, like the every six months intervals used in the provided exercise.
• Organize the data for easy observation, often accomplished through a time-series plot.
• Observe the progression of the data to recognize any upward or downward patterns.

In the exercise, we notice an upward trend in wireless substitution. From 2005 to 2008, the percentage of homes with only wireless service steadily increases. A consistent increase indicates that each period sees more homes making the switch. This is especially clear given the relatively smooth upward trajectory observed in the plotted points.

Data Visualization

Data visualization is essential for interpreting complex datasets in an easily understandable way. It involves creating visual representations of data to highlight trends and patterns. In the context of wireless substitution, a time-series plot is a powerful tool for illustrating changes over time. Creating an effective time-series plot involves:

• Using an x-axis to represent time and a y-axis to show the percentage of homes with wireless service.
• Plotting each (date, percentage) pair to illustrate changes over time.
• Drawing lines between successive data points to make the trend more visually apparent.

With our data, the plot reveals a clear upward trend, making it straightforward to interpret the increasing adoption of wireless phones. By using visual tools, the course of change becomes more apparent than simply reading numerical data, thus aiding in quick and effective decision-making processes.