Question

According to estimates from the federal government's 2003 National Health Interview Survey, based on face-to-face interviews in 16,677 households, approximately \(58.2 \%\) of U.S. adults have both a landline in their residence and a cell phone, \(2.8 \%\) have only cell phone service but no landline, and \(1.6 \%\) have no telephone service at all. a) Polling agencies won't phone cell phone numbers because customers object to paying for such calls. What proportion of U.S. households can be reached by a landline call? b) Are having a cell phone and having a landline independent? Explain.

Short answer

a) 95.6% can be reached by landline. b) Not independent, as probabilities differ.

Step-by-step solution

Understand the Given Data

We are given that 58.2% households have both a landline and a cell phone, 2.8% have only a cell phone, and 1.6% have no phone at all. The sum of these percentages covers all households.

Calculate Households Reachable by Landline

We need to find the proportion of households with at least a landline. Since 58.2% have both and the rest either have only a landline or neither, we subtract the cell-only and no-service percentages from the total 100%. This gives us: \[ 100\% - 2.8\% - 1.6\% = 95.6\% \] Thus, 95.6% of households can be reached by landline.

Evaluate Independence of Landline and Cell Phone

For two events (having a cell phone and having a landline) to be independent, the probability of having both should equal the product of individual probabilities.Probability of having a cell phone: \( 58.2\% + 2.8\% = 61\% \)Probability of having a landline: \( 100\% - 1.6\% = 98.4\% \)Probability of both if independent: \[ 0.61 \times 0.984 = 0.60024 = 60.024\% \]Since the calculated 58.2% is not equal to 60.024%, having a cell phone and a landline are not independent.

Key concepts

Independence of Events

In probability theory, events are considered independent if the occurrence of one does not affect the probability of the other. For example, flipping a coin does not influence the roll of a die. When exploring household communications, the independence of having a landline and having a cell phone is intriguing. If these events were independent, the occurrence of both should equal the product of their individual probabilities.

From the survey data, 61% of households have a cell phone and 98.4% have a landline. If these means of communication were independent, the probability of having both would be 0.61 times 0.984, which results in 60.024%. However, this does not match the actual data, which reports only 58.2% with both. This discrepancy indicates dependence, showing that having one affects the likelihood of having the other.

Understanding such relationships is crucial in interpreting survey results. It highlights that owning a cell phone might influence decisions about landline use, a key insight for marketers and policymakers.

Survey Data Analysis

Survey data analysis is a powerful tool in understanding behavioral patterns and preferences. It often involves collecting data from a sample of individuals and extrapolating to a larger population. Here, the National Health Interview Survey provides insights into telephone usage among US adults.

One of the primary goals of analyzing such surveys is to determine proportions within a population. For instance, we are provided with the percentages of households having specific phone services. Calculations reveal the reach of services like landlines, giving pollsters a better understanding of how to contact individuals for future surveys. These insights drive decisions on communication strategies and reveal societal trends.

Analyzing survey data involves checking for errors, verifying data against known results, and performing statistical calculations. It forms the backbone of decisions in business and government regarding resources and strategies. Understanding how to interpret and calculate from survey data is a valuable skill for anyone involved in data-driven decision-making.

Household Telephone Statistics

Household telephone statistics offer a snapshot of technological penetration in homes. They reveal how communication methods evolve, providing crucial data for industries like telecommunication providers and marketing agencies.

In the survey data, the breakdown provides insights such as 58.2% of households having both landline and cell phone services. It also highlights more unusual groups, like the 2.8% with only a cell phone and the 1.6% without any service at all. These statistics help companies understand market saturation and areas where services might be expanded or adjusted.

Moreover, these statistics inform about reaching out to customers. For instance, knowing that 95.6% of households can be reached by landline allows pollsters and businesses to strategize their outreach effectively. Understanding these statistics is key in planning marketing campaigns, service offerings, and engaging with a broad audience in an efficient manner.