Question

1. The tax officials at the Internal revenue Service (IRS) are constantly working toward improving the wording and format of the tax returns. As part of a larger effort to help taxpayers, the Internal Revenue Service plans to streamline one of the forms into a shorter and simpler form for the 2021 tax season.

2. Upon successful completion of this exercise, the new form, – about half the size of the current version – would replace the previous ones and will be shared with the tax community for the feedback. The new Form uses a “building block” approach, in which the tax return is reduced to a simple form. That form can be supplemented with additional schedules if needed. Taxpayers with straightforward tax situations would only need to file this new form with no additional schedules.

To finalize this exercise, the IRS have developed three new forms, and to determine which, if any, are superior to the current forms, 120 individuals were asked to participate in an experiment. Each of the three new forms and the currently used form were filled out by 30 different people. The amount of time (in minutes) taken by each person to complete the task was recorded. The data collected is attached in the Excel file named: Tax Forms worksheet.

You are expected to analyze the project in two phases:

Phase1:

1. a) Describe the problem background, objective of study and identify the type of scale of measurement for the data

2. b) Use appropriate descriptive statistics to explore and summarize the data for Tax form 2 & 3 and compare their results. Remember to interpret the findings accurately and present them in a clear and coherent way.

3. c) Assuming data for Form 2 is normally distributed, calculate the parentage of people who completed the form between 83.9 and 107.5 minutes (round the descriptive statistics numbers to one decimal)

4. d) If the filling time of all IRS forms is distributed normally with mean of 102 and standard deviation of 8, what is the probability that a randomly selected person could do the tax forms in less than 90 minutes?

e) Referring to problem “d” above, If a randomly selected person is in the top 5 percent of the fastest people who do the tax forms, at least how many minutes should he spent to fill out the form?

"Excel sheet numbers:

Taxpayer Form 1 ------Form 2------- Form 3 ------Form 4

1-------------- 109 ------------115 ----------126 -----------120

2-------------- 98 -------------103 ----------107 -----------108

3 -------------29 --------------27------------ 53------------- 38

4------------ 93 ---------------95 ------------103---------- 109

5------------ 62--------------- 65------------ 67------------- 64

6 -----------103------------- 107----------- 111----------- 128

7------------ 83-------------- 82------------ 101------------ 116

8------------ 122------------ 119----------- 141----------- 143

9 -------------92------------ 101----------- 105------------ 108

10------------ 107--------- 113------------- 127----------- 113

11------------ 103---------- 111------------ 111------------ 108

12------------ 54------------ 64-------------- 67-------------62

13------------ 141---------- 145----------- 142------------160

14------------ 92------------ 94------------- 95-------------102

15 ------------29 -----------32------------- 33---------------62

16----------- 83------------- 83------------ 89-------------- 86

17------------ 34 -----------36 ------------40---------------48

18 ------------83----------- 86------------- 90-------------119

19------------ 157---------- 157----------- 172-----------193

20------------- 99---------- 107------------- 111-----------100

21----------- 118----------- 123------------- 117----------130

22------------ 58----------- 65--------------- 75-------------81

23 ------------66----------- 71---------------- 79------------81

24------------ 60----------- 60--------------- 78------------ 41

25 ------------102---------- 106------------ 100---------- 142

26 -------------128---------- 134------------ 135--------- 142

27---------------87---------- 93------------- 90------------ 77

28--------------126-------- 134----------- 129----------- 154

29----------- -133---------- 130----------- 148----------- 164

30------------ 100----------- 112---------- 107----------- 120

Answer 1

a)

Problem background: Sometimes use of use complex words and format of the tax return form cause a delay in ITR filling so the tax officials work constantly to overcome these issues. In this study, the

The objective of the study is to test whether the new form significantly reduces the time to fill it compared to the previous one.

The scale of measurement: The variable of interest is the time taken to fill the form hence the time is measured at the ratio level of measurement because the absolute zero is defined and the difference between values is meaningful.

b)

The descriptive statistic values for form 2 and form 3 are obtained in excel in the following steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Descriptive Statistic. The screenshot is shown below,

Step 1: Input Range: Form 2 and Form 3 column, Grouped By: Columns, tick Summary Statistic. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

From the data values,

mean < median

skewness = -ve

From the table, we can see that the mean value is slightly less than the median and the skewness value is -ve which indicates the distribution is slightly skewed to left (negatively skewed). Since the distribution is slightly skewed we can take an assumption that the distribution of population is normal.

c)

From the table,

Form 2

Mean	95.6667
Standard Deviation	32.5739
Count	30

The probability is obtained by calculating the z score,

The probability is obtained from the z distribution table. In excel use the function =NORM.S.DIST()

d)

For all the form,

Mean	102
Standard Deviation	8

The probability is obtained by calculating the z score,

The probability is obtained from the z distribution table.

e)

For the top 5%

The z score for the probability = 0.95 is obtained from the standard normal distribution table. In excel use function =NORM.S.INV().

I will take approximately 115 minutes.