Suffolk County Community College

### Question Description

I don’t understand this Mathematics question and need help to study.

please help with statistics learning binder

Outline is below

Only for chapters 3-6 for now

I will upload the pictures of the textbook from chapters 1-2 so you can Do it

Answer all questions 1-10 for each chapter

Don’t just copy and plagiarie from textbook use your own words you can copy the multiple choice questions from each chapter though

I am not sure how many pages it will be but it may be 2-3 pages each chapter I think thank you

16 days ago

## Final Answer

hey here it is. please look it over and let me know if its ok

Running head: CHAPTER 6

1

Chapter 6

Student’s Name

Institution

Date

CHAPTER 6

2

Chapter 6: Chi-Square Tests

Contingency Tables

The introduction of this topic has given an example of a contingency table and how data

is arranged in the table. A contingency table is an array of data displayed in a matrix format of

rows and columns showing the frequency distribution of the respective variables. The purpose of

the contingency table is to determine whether there is a dependence between two variables.

Additionally, the contingency table can be used to calculate the probability of the individual

variables.

Motivating the Chi-square Test of Independence

In a statistical experiment, two sets are independent if they occur exclusively. Therefore,

one event does not affect the occurrence of another event. In a contingency table, the observed

frequencies indicate the actual number of the values while the expected frequencies indicate the

expected number assuming independence of the observed variables.

Making an Inference About a Population from a Sample

In this topic, the authors have revisited the hypothesis testing. In statistics, the null

hypothesis indicates the existence of no significance between the observed variables, while the

null hypothesis suggests the existence of significance between the observed variables. Therefore,

there are only two possible decisions for the test of independence. Rejecting the null hypothesis

indicates the existence of significance while failing to reject the null hypothesis suggests

significance between the observed variables, in this case, dependence. Furthermore, the topic has

restated that type I error is an error due to rejecting the null hypothesis when it is true while type

CHAPTER 6

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II error occurs due to failing to reject the null hypothesis when it is false. The null hypothesis is

symbolized as H0, while the alternative hypothesis is represented as H1 or Ha.

Pearson's Chi-Square Test Statistic

Pearson's Chi-square test statistic (X2) is the statistical test applied in a contingency table

to determine whether the observed values occurred by chance or if there exists variation in the

data. In computing the expected frequencies in the contingency table, the values must be at least

five. Where the values are less than five, two or more rows have to be combined with having a

value greater than five. The chi-square test statistic is given by [(O-E)2/E], where O is the

observed frequency and E the expected frequency.

Interpreting the Test Statistic: The Null Distribution

After computing the test statistic, it is essential to determine whether it warrants rejecting

the null hypothesis. This is checked against the degrees of freedom given by DF = (r-1) (c-1)

where r is the number of rows and c the number of columns. When making inferences using

Pearson's chi-square test statistics, we reject the null hypothesis if the value of the calculated test

statistic is greater than or equal to the critical value. The critical value can be obtained from

statistical tables.

Vocabulary Terms

Chi-square test. A statistical test applied in a contingency table to determine whether the

observed values occurred by chance or if there exists variation in the data.

Contingency table. An array of data displayed in a matrix format of rows and columns

showing the frequency distribution of the respective variables.

CHAPTER 6

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Null hypothesis. A hypothesis stating no statistical significance between the observed

variables.

Alternative hypothesis. A hypothesis stating statistical significance between the

observed variables.

Memorization Strategy

To memorize the vocabulary terms learned in this chapter, I composed a tune that

summarized the meaning of these terms as well as how they are applied. Furthermore, most of

the terms learned in this chapter were covered in the previous topics hence was able to master

within two days.

Multiple Choice Questions

1. A researcher wishes to perform some statistical procedures. These procedures only work

properly if the data is randomly selected from a normal population. Upon these data, she

performs a Shapiro-Wilk test. Her expensive statistical package reports a p-value of

0.567788.

I.

At the 5% significance level, it is appropriate to use her data for the purposes she

set forth.

II.

At the 1% significance level, it is appropriate to use her data for the purposes she

set forth.

a. I is true, and II is true.

b. I is true, and II is false....