Tax Survey. A random telephone survey of 1021 adults (aged...

Tax Survey. A random telephone survey of 1021 adults (aged 18 and older) was conducted by Opinion Research Corporation on behalf of CompleteTax, an online tax preparation and e -filing service. The survey results showed that 684 of those surveyed planned to file their taxes electronically (Complete Tax Tax Prep Survey). a. Develop a descriptive statistic that can be used to estimate the percentage of all taxpayers who file electronically. b. The survey reported that the most frequently used method for preparing the tax return is to hire an accountant or professional tax preparer. If $60 \%$ of the people surveyed had their tax return prepared this way, how many people used an accountant or professional tax preparer? c. Other methods that the person filing the retum often used include manual preparation, use of an online tax service, and use of a software tax program. Would the data for the method for preparing the tax return be considered categorical or quantitative?

Tax Survey. A random telephone survey of 1021 adults (aged 18 and older) was conducted by Opinion Research Corporation on behalf of CompleteTax, an online tax preparation and e -filing service. The survey results showed that 684 of those surveyed planned to file their taxes electronically (Complete Tax Tax Prep Survey).
a. Develop a descriptive statistic that can be used to estimate the percentage of all taxpayers who file electronically.
b. The survey reported that the most frequently used method for preparing the tax return is to hire an accountant or professional tax preparer. If $60 \%$ of the people surveyed had their tax return prepared this way, how many people used an accountant or professional tax preparer?
c. Other methods that the person filing the retum often used include manual preparation, use of an online tax service, and use of a software tax program. Would the data for the method for preparing the tax return be considered categorical or quantitative?

Key Concepts

Descriptive Statistics

Descriptive statistics involve summarizing or describing features of a dataset, which includes calculating measures such as proportions, percentages, and averages. In survey research, these statistics offer a comprehensive overview of the responses and allow for an estimation of the characteristics of the entire population based on the data collected.

Sample Proportion

A sample proportion is the fraction of a sample that meets a specific condition, calculated by dividing the count of individuals with that characteristic by the total sample size. This proportion serves as an estimate for the analogous percentage in the broader population, making it essential for inferring population-level trends from survey data.

Calculating Frequencies Using Percentages

When survey results are reported in percentages, converting these percentages into actual counts involves multiplying the percentage (expressed as a decimal) by the total number of respondents. This process is important in understanding the scale of the results and contextualizing percentage figures into concrete numbers.

Categorical Data

Categorical data consists of values that represent distinct groups or categories, rather than quantities. In the context of survey responses, methods of preparing a tax return, such as hiring a professional versus using software or online services, are examples of categorical data where each method is a nominal category without inherent numerical magnitude.

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