91Ó°ÊÓ

For each of the following situations, state whether the parameter of interest is a mean or a proportion. (a) A poll shows that \(64 \%\) of Americans personally worry a great deal about federal spending and the budget deficit. (b) A survey reports that local TV news has shown a \(17 \%\) increase in revenue within a two year period while newspaper revenues decreased by \(6.4 \%\) during this time period. (c) In a survey, high school and college students are asked whether or not they use geolocation services on their smart phones. (d) In a survey, smart phone users are asked whether or not they use a web- based taxi service. (e) In a survey, smart phone users are asked how many times they used a web- based taxi service over the last year.

Step by step solution

01

- Define Parameter of Interest for Situation (a)

For (a), the information provided is about the percentage of Americans who worry about federal spending and the budget deficit. Since this describes a percentage of the population, the parameter of interest is a proportion.

02

- Define Parameter of Interest for Situation (b)

For (b), we are looking at changes in revenue over two years. The numbers reported (17% increase and 6.4% decrease) relate to changes in quantities over time, which suggests we are dealing with a mean. Such change typically reflects a difference in average revenue amounts over the specified period.

03

- Define Parameter of Interest for Situation (c)

In (c), each student is either using geolocation services or not. This 'yes or no' data is countable and results in binary outcomes, meaning the parameter of interest is a proportion.

04

- Define Parameter of Interest for Situation (d)

In (d), smart phone users respond ‘yes’ or ‘no’ to using a web-based taxi service. This reflects categorical data, where we are interested in counting the proportion of users who use such a service.

05

- Define Parameter of Interest for Situation (e)

For (e), the survey asks how many times smart phone users used a web-based taxi service in the previous year. Here, the data collected is quantitative, describing an average count or mean usage.

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Key Concepts

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

Parameter of Interest

In statistics, the "parameter of interest" refers to the specific summary characteristic or measure that a researcher desires to learn about a population. This could be either a mean (average) or a proportion (percentage).
Understanding the parameter of interest is crucial for determining the correct statistical approach.

• When the parameter of interest is a mean, we're typically dealing with quantitative data, which provides numerical values indicating how much or how many of something is present.
• Conversely, a proportion pertains to categorical data, which gives us percentages or ratios indicating how often or how prevalent an attribute or condition is within a group.

For example, in a survey asking participants how many times they took a taxi, the parameter of interest is a mean, because it involves calculating an average frequency. Meanwhile, with questions seeking a 'yes' or 'no' response, such as whether participants worry about a specific issue, the parameter of interest is a proportion, as this deals with the percentage of affirmative responses in the population.

Mean and Proportion

Understanding mean and proportion is paramount in making informed inferences about populations based on sample data.

• The mean provides information about the central tendency of data. It sums all observations and divides by the number of observations. This is particularly relevant in quantitative analyses, such as finding average revenue changes or average service usage over time.
• The proportion, on the other hand, conveys the fraction of the population that exhibits a certain characteristic. This is vital in categorical analyses, such as determining what percentage of a population supports a policy or uses a specific service.

In our examples, consider situation (e) where users report the number of times they use a taxi service. Here, finding the mean use helps summarize the data, indicating the typical behavior among users. In contrast, situation (c) involves a yes/no question about geolocation usage, where the proportion of affirmative responses is the focus.

Survey Analysis

Survey analysis is the practice of examining survey data to extract meaningful insights. Whether dealing with means or proportions, analyzing survey data can reveal important information about public opinion, behavior, or trends. Successful survey analysis follows these fundamentals:

• Data Collection: Ensure comprehensive and reliable data acquisition, often via questionnaires or structured interviews.
• Data Processing: Clean and organize the data for analysis, removing any anomalies or errors.
• Statistical Analysis: Employ appropriate statistical techniques to explore and interpret the results. Here, differentiating between means and proportions is essential to apply the correct methods.
• Result Interpretation: Convert statistical findings into comprehensible insights for decision-making or policy formation.

In scenario (b), analyzing the change in local TV news revenue involves calculating a mean to showcase average growth over time. For scenario (a), determining the proportion of the population that worries about federal spending provides a clear snapshot of public concern. By analyzing such results, organizations can make data-informed decisions that align plans with emerging trends or public sentiment.