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Sampling Greenville County. The rails to trails program involves the conversion of old rail corridors into multipurpose trails for recreation and transportation. Researchers were interested in obtaining information on characteristics of users and nonusers of a 10 -mile-long paved greenway trail in Greenville, South Carolina, that connects residential areas to both a university campus and the commercial downtown area of the city. Random digit dialing of residential numbers was done using a database of exchanges. A total of 2461 persons were contacted, and 726 of them completed the survey. When a household was reached, surveyors asked to speak to the adult over 18 with the next birthday. No cell phone numbers \(\mathrm{~ w e r e ~ i n c l u d e d ~ i n ~ t h e ~ s a m p l e . ? ? ?}\) a. What is the population of interest? What is the response rate for the survey? b. The following table gives the number of adults between 18 and 64 and over 65 in both the sample and the county (only 689 of the 726 respondents to the survey provided data on their ages). The county counts were obtained from the U.S. Census Bureau: What percentage of the sample is between 18 and 64? What percentage of the population is between 18 and 64? Does this difference surprise you, given the sampling method described? Explain briefly. c. Among the 726 respondents, 181 , or \(24.9 \%\), reported having used the trail in the past six months. Do you think this sampling method gives biased information about the percentage of Greenville County adults who have used the trail in the past six months? What is the likely direction of bias? Explain briefly.

Step by step solution

01

Determine the Population of Interest

The population of interest consists of all adults in Greenville County who live in residences with landline telephones. They are the primary group the researchers wanted to gather data from.

02

Calculate the Response Rate

The response rate can be calculated using the formula: \( \text{Response Rate} = \frac{\text{Number of Completed Surveys}}{\text{Total Number of Contacts}} \times 100 \). Here, it is \( \frac{726}{2461} \times 100 \approx 29.5\% \).

03

Calculate the Sample Percentage for Ages 18-64

Given that 689 respondents provided their ages, you can use this number to calculate the percentage of respondents between 18 and 64 years old. The number of respondents in this age group is provided in a table within the exercise prompt.

04

Calculate the Population Percentage for Ages 18-64

Use population data from the table provided and calculate the percentage of the population in the 18 to 64 age range based on U.S. Census Bureau data.

05

Compare Sample and Population Percentages

Analyze whether the percentage in the sample group (18-64 years old) is notably different from the population percentage. Explain whether the difference is expected, considering the sampling method used, which excludes cell phones and works through landline connections.

06

Discuss Sampling Method Bias

Given that 181 out of 726 respondents used the trail, consider if the sampling method might bias this result. Since surveys were conducted via landline, the likely bias results from an older population sample, possibly under-representing younger residents who might be more inclined to use the trail. The direction of bias could potentially underestimate trail usage frequency.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Response Rate

The response rate is a key metric in surveys that indicates the percentage of people who completed the survey out of those who were contacted. It tells us how many of the people reached were willing to participate and present their views or experiences.

In this exercise, 726 out of 2461 people contacted completed the survey. To find the response rate, you can use the formula: \( \text{Response Rate} = \frac{\text{Number of Completed Surveys}}{\text{Total Number of Contacts}} \times 100 \).

Applying the numbers: \( \frac{726}{2461} \times 100 \approx 29.5\% \).

This response rate is quite typical in telephone surveys, where people might be busy or uninterested. A higher response rate is generally better as it suggests a more representative view of the population.

Population of Interest

Understanding the population of interest is crucial for interpreting survey results. It refers to the group of individuals that the researchers aim to draw conclusions about based on their study.

In the case of Greenville County's exercise, the population of interest includes all adults in Greenville County living in residences with landlines. This group is the focus because they are who the surveyors aimed to gather opinions from.

However, this definition also introduces potential bias, as excluding cell phone users might omit a significant portion of the population, particularly younger adults who prefer mobile communication.

Sampling Bias

Sampling bias occurs when certain members of the intended population are less likely to be included in the sample, leading to results that can skew towards a subset rather than reflect true diversity.

In this scenario, the use of landline phone calls to survey participants likely results in a sampling bias. This method tends to reach older individuals who maintain landlines and may not accurately represent younger demographics, who are more inclined to use cell phones.

As a result, the respondents in the selected sample may not accurately reflect the population's behavior or opinions, such as the actual percentage of people using the greenway trail.

Age Demographics

Age demographics in a survey are crucial for understanding the composition of respondents and how it compares to broader population metrics.

In this study, we evaluate age groups by comparing the percentage of respondents aged 18 to 64 with the U.S. Census Bureau data for the same age group. Such comparisons reveal disparities between the sample and the broader population.

If the sample has fewer respondents in the younger age bracket (18-64) than expected, given the Census data, it suggests that younger individuals might be underrepresented. This underrepresentation can affect conclusions drawn about the entire population, especially concerning activities like trail usage, which might be more popular among younger people.