Question D)Question E) Problem 3: Tax Preparation Savings?Every year, Americans fill out their tax return forms (this year, Tax Day was moved until May17). A new tax preparation company wanted to advertise that their company would save theaverage individual money compared to an individual using an online tax preparation software.To determine if there was evidence to support their claim, the company decided to conduct anexperiment. In the experiment, a random sample of 15 American tax filers was selected and theirtaxes were prepared by the company's most senior accountant as well as from the software (bothfree of charge). To keep the software preparation uniform, one independent accountant preparedeach of the 15 tax filers' taxes in the same way without knowledge of the company's work. Thedata set is called “Tax Preparation Savings" and data are presented in dollars. Negative valuesare the amount an individual tax filer would have to pay. Assume all conditions hold and use asignificance level of 0.10 when you test the hypothesis.a) Calculate the difference between the company results and the software result for eachindividual tax filer, (subtract Company – Software) using StatCrunch. List the differencefor each of the pairs in one column in your solutions document.b) Obtain the sample mean of these differences and the sample standard deviation of thesedifferences in StatCrunch. Copy the table that you obtain from StatCrunch and round thevalues to two decimal places.c) Define the population parameter in context in one sentence.d) State the null and alternative hypotheses using correct notation.e) Calculate the test statistic. Please do this "by hand" using the formula and showing yourwork (please type your work). Use the values you obtained in part (b). Round the teststatistic to three decimal places.f) Calculate p-value using the T-calculator in StatCrunch (STAT → Calculators → T).Use the correct probability notation as you present your answer. In addition, state thedegrees of freedom for this test and how these were calculated.g) Use StatCrunch Stat > T Stats > Paired and enter Company for Sample 1 andSoftware for Sample 2 to verify your test statistic from part (e) and your p-value in part(). Copy the output into your document.h) State your decision whether you reject or do not reject the null hypothesis and the reasonfor your decision in one sentence.i) State your conclusion in context of the problem in one or two complete sentences. StatCrunchTax Preparation SavingsStatCrunch - Applets - Edit - Data - Stat - Graph - Help -RowCompanySoftwarevar3var4var5var61-4392-43212339546312941344433392921-998-1009-2835-21937166210248.-49-2349.1001885103065199711-3298-4072121682341353939214-1279-134515102-102161718192021222324252627282930

Name: Question D)Question E) Problem 3: Tax Preparation Savings?Every year,
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Note: Hey there! Thank you for the question. As you have specifically mentioned parts d and e, we…

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d) State the null and alternative hypotheses using correct notation. e) Calculate the test statistic. Please do this “by hand" using the formula and showing your work (please type your work). Use the values you obtained in part (b). Round the test statistic to three decimal places.

d) State the null and alternative hypotheses using correct notation. e) Calculate the test statistic. Please do this “by hand" using the formula and showing your work (please type your work). Use the values you obtained in part (b). Round the test statistic to three decimal places.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.

Topic Video

Question

Question D)

Question E)

Problem 3: Tax Preparation Savings?
Every year, Americans fill out their tax return forms (this year, Tax Day was moved until May
17). A new tax preparation company wanted to advertise that their company would save the
average individual money compared to an individual using an online tax preparation software.
To determine if there was evidence to support their claim, the company decided to conduct an
experiment. In the experiment, a random sample of 15 American tax filers was selected and their
taxes were prepared by the company's most senior accountant as well as from the software (both
free of charge). To keep the software preparation uniform, one independent accountant prepared
each of the 15 tax filers' taxes in the same way without knowledge of the company's work. The
data set is called “Tax Preparation Savings" and data are presented in dollars. Negative values
are the amount an individual tax filer would have to pay. Assume all conditions hold and use a
significance level of 0.10 when you test the hypothesis.
a) Calculate the difference between the company results and the software result for each
individual tax filer, (subtract Company – Software) using StatCrunch. List the difference
for each of the pairs in one column in your solutions document.
b) Obtain the sample mean of these differences and the sample standard deviation of these
differences in StatCrunch. Copy the table that you obtain from StatCrunch and round the
values to two decimal places.
c) Define the population parameter in context in one sentence.
d) State the null and alternative hypotheses using correct notation.
e) Calculate the test statistic. Please do this "by hand" using the formula and showing your
work (please type your work). Use the values you obtained in part (b). Round the test
statistic to three decimal places.
f) Calculate p-value using the T-calculator in StatCrunch (STAT → Calculators → T).
Use the correct probability notation as you present your answer. In addition, state the
degrees of freedom for this test and how these were calculated.
g) Use StatCrunch Stat > T Stats > Paired and enter Company for Sample 1 and
Software for Sample 2 to verify your test statistic from part (e) and your p-value in part
(). Copy the output into your document.
h) State your decision whether you reject or do not reject the null hypothesis and the reason
for your decision in one sentence.
i) State your conclusion in context of the problem in one or two complete sentences.

StatCrunch
Tax Preparation Savings
StatCrunch - Applets - Edit - Data - Stat - Graph - Help -
Row
Company
Software
var3
var4
var5
var6
1
-4392
-4321
2
339
546
3
1294
1344
4
3339
2921
-998
-1009
-2835
-2193
7
1662
1024
8.
-49
-234
9.
1001
885
10
3065
1997
11
-3298
-4072
12
168
234
13
539
392
14
-1279
-1345
15
102
-102
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

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