A random telephone survey of 1021 adults (aged 18 and older)...

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 (CompleteTax Tax Prep Survey 2010 ). 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 retumis 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?

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 (CompleteTax Tax Prep Survey 2010 ).
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 retumis 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 refer to the methods used to summarize and describe the characteristics of a set of data. In this context, it involves calculating a statistic such as a proportion or percentage that provides insight into the behavior or attribute of a group, like the percentage of taxpayers who file electronically.

Proportion Estimation

Proportion estimation is a technique used in statistics to estimate the fraction or percentage of the total population that exhibits a particular attribute, based on data from a sample. Here, the proportion of adults filing electronically is estimated by dividing the number of affirmative responses by the total sample size.

Data Types - Categorical vs. Quantitative

Understanding data types is fundamental in statistics. Categorical data refers to values that represent distinct groups or categories, such as the method used to prepare taxes. Quantitative data, on the other hand, consists of numerical values that represent measurable quantities. Determining the nature of data helps in choosing the correct analysis method.

Frequency Counts

Frequency counts are a basic descriptive tool that involves tallying the number of occurrences of each category or response within a dataset. In surveys, frequency counts show how often each method or response is reported, which is crucial for understanding the distribution of different responses.

Transcript

00:02 Hey everyone, today we're solving problem number 18 from chapter one of the textbook.

00:09 This is dealing with descriptive statistics.

00:14 So in the first part, you are asked to develop a descriptive statistic that essentially talks about something about taxpayers.

00:23 And you're given the total of 1 ,024 adults as your sample size.

00:29 And you're told that 684 manually, file, i mean electronically file, excuse me, for taxes, and then the rest, manually file.

00:40 So i'm just going to make a little table for myself, so i know that i have electronic, so i'll just write e, and then i have manual, and then i have my total, right? again, that's for method of processing my taxes, or filing that, excuse me.

01:00 Then i have my totals that they give.

01:03 They give $684 .84.

01:08 They tell you that.

01:11 They tell you the total surveyed was $1 ,021.

01:16 So sample size, just so you all know for statistics, sample size is usually labeled by the variable n in case that ever comes up.

01:23 And we don't know what this is right here for how many manually filed.

01:27 Something else we do know is that the total for percentages, which we're going to have to use for this problem, because it asks us to develop a descriptive statistic to represent percentages.

01:40 We know that total always has to be 100%.

01:42 So i'm making a mini table here, guys.

01:47 There, there, there, there.

01:54 All right.

01:54 So i know there's a total of 1 ,021 people surveyed in this particular survey.

02:00 And i know 684 electronically do it.

02:03 So i just simply do 1 ,021 minus 684 to find out how many manually filed their taxes, and i get 337.

02:12 Percentages are going to be very easy.

02:14 So we'll go to the right now.

02:16 So i know that i have 684 electronically over a total of 1224.

02:20 So what i'm going to do for percentages is you always devise.

02:24 You do 684 divided by 1 .021.

02:27 And i get 0 .6699 and multiply that by 100 to get my percentage.

02:31 Remember percentage is out of 100.

02:33 So you have to multiply by 100.

02:35 And i get 66 .99%.

02:41 So that's actually you to be your final.

02:43 Answer.

02:47 They can circle that for the time being.

02:49 And then i know that i have a total 100%, again, this is rounded, by the way, 6 .99 to two decimal places.

02:55 So i do 100, the total minus 6 .99 amount that electronically did it, the percentage of electronic did it.

03:02 And when i do that, i get 33 .01 % of the people surveyed manually filed taxes.

03:10 So we're asked to develop a descriptive statistics.

03:15 So we are dealing with categorical data because it's either they manually or electronically did it.

03:19 So there's two different options given to them.

03:22 There's no numerical values that represent how much or how many of something.

03:27 So it can't at all be quantitative.

03:28 It has to be categorical.

03:30 When you're doing categorical data, typically bar graphs or pie charts are the way to represent data...

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