# Category: Testing of Hypothesis

Testing of Hypothesis, Hypothesis testing, Independent t test, Independent z test, Analysis of variance, ANOVA, Comparison tests

## Online Quiz Hypothesis Testing

Multiple Choice Questions (Online Quiz Hypothesis Testing and Estimation) from Statistical Inference for the preparation of exams and different statistical job tests in Government/ Semi-Government or Private Organization sectors. These tests are also helpful in getting admission to different colleges and Universities. The Estimation and Hypothesis Testing Quiz will help the learner to understand the related concepts and enhance the knowledge too.

Most of the MCQs on this Post cover Estimate and Estimation, Testing of Hypothesis, Parametric and Non-Parametric tests, etc.

## Chi-Square Association Quiz – 2

The relationship/ dependency between the attributes is called association and the measure of degrees of relationship between the attributes is called the coefficient of association. The Chi-Square Statistic is used to test the association between the attributes. The Chi-Square Association is defined as

$$\chi^2 = \sum \frac{(of_i – ef_i)^2}{ef_i}\sim \chi^2_{v},$$

where $v$ denotes the degrees of freedom

The following is the MCQs Association Test

The quiz about Chi-Square Association between attributes.

1. For $3\times 3$ contingency table the degrees of freedom is

2. If $\chi^2_c=5.8$ and $df=1$, we make the following decision ———-.

3. Association measures the strength of the relationship between

4. A characteristic which varies in quality from one individual to another is called

5. If $(AB) > \frac{(A)(B)}{n}$ then association is

6. The presence of an attribute is denoted by

7. The parameter of the Chi-Square distribution is ———–.

8. The coefficient of association $Q$ lies between

9. For $r\times c$ contingency table, the Chi-Square test has $df=$ ———-.

10. The eye colour of 100 men is

11. The value of $\chi^2$ cannot be ———.

12. There are ———– parameters of Chi-Square distribution.

13. The process of dividing the objects into two mutually exclusive classes is called

14. Two attributes $A$ and $B$ are said to be positively associated if

15. If $(AB) < \frac{(A)(B)}{n}$ then association between two attributes $A$ and $B$ is

16. If for a contingency table $df=12$ and number of rows is 4 then the number of columns will be

17. A contingency table with $r$ rows and $c$ columns is called

18. A $4 \times 5$ contingency table consists of ———.

19. Two attributes $A$ and $B$ are said to be independent if

20. The range of $\chi^2$ is

A population can be divided into two or more mutually exclusive and exhaustive classes according to their characteristics. It is called dichotomy or twofold division if it is divided into two mutually exclusive classes. A contingency table is a two-way table in which the data is classified according to two attributes, each having two or more levels. A measure of the degree of association between attributes expressed in a contingency table is known as the coefficient of contingency. Pearson’s mean square coefficient of contingency is

$C=\sqrt{\frac{\chi^2}{n+\chi^2}}$

Attributes are said to be independent if there is no association between them. Independence means the presence or absence of one attribute does not affect the other. The association is positive if the observed frequency of attributes is greater than the expected frequency and negative association or disassociation (negative association) is if the observed frequency is less than the expected frequency.

Perform another Non-Parametric Test: MCQs Non-Parametric

## MCQs Chi-Square Association

This post is about MCQs on Chi-Square Association.
The relationship/ Dependency between the attributes is called association and the measure of degrees of relationship between the attributes is called the coefficient of association. The Chi-Square Statistic is used to test the association between the attributes. The Chi-Square Association is defined as

$$\chi^2 = \sum \frac{(of_i – ef_i)^2}{ef_i}\sim \chi^2_{v},$$

where $v$ denotes the degrees of freedom

The following is the MCQs Chi-Square Association Test

Please go to MCQs Chi-Square Association to view the test

Attributes are said to be independent if there is no association between them. Independence means the presence or absence of one attribute does not affect the other. The association is positive if the observed frequency of attributes is greater than the expected frequency and negative association or disassociation (negative association) is if the observed frequency is less than the expected frequency.

Perform another Non-Parametric Test: MCQs Non-Parametric

## Contingency Tables | Cross Classification: Introduction

Contingency Tables also called cross tables or two-way frequency tables describes the relationship between several categorical (qualitative) variables. A bivariate relationship is defined by the joint distribution of the two associated random variables.

Contingency Tables

Let $X$ and $Y$ are two categorical response variables. Let variable $X$ have $I$ levels and variable $Y$ have $J$ levels. The possible combinations of classifications for both variables are $I\times J$. The response $(X, Y)$ of a subject randomly chosen from some population has a probability distribution, which can be shown in a rectangular table having $I$ rows (for categories of $X$) and $J$ columns (for categories of $Y$). The cells of this rectangular table represent the $IJ$ possible outcomes. Their probability (say $\pi_{ij}$) denotes the probability that ($X, Y$) falls in the cell in row $i$ and column $j$. When these cells contain frequency counts of outcomes, the table is called a contingency or cross-classification table and it is referred to as a $I$ by $J$ ($I \times J$) table.

The probability distribution {$\pi_{ij}$} is the joint distribution of $X$ and $Y$. The marginal distributions are the rows and columns totals obtained by summing the joint probabilities. For the row variable ($X$) the marginal probability is denoted by $\pi_{i+}$ and for column variable ($Y$) it is denoted by $\pi_{+j}$, where the subscript “+” denotes the sum over the index it replaces; that is, $\pi_{i+}=\sum_j \pi_{ij}$ and $\pi_{+j}=\sum_i \pi_{ij}$ satisfying

$l\sum_{i} \pi_{i+} =\sum_{j} \pi_{+j} = \sum_i \sum_j \pi_{ij}=1$

Note that the marginal distributions are single-variable information, and do not pertain to association linkages between the variables.

In (many) contingency tables, one variable (say, $Y$) is a response, and the other $X$) is an explanatory variable. When $X$ is fixed rather than random, the notation of a joint distribution for $X$ and $Y$ is no longer meaningful. However, for a fixed level of $X$, the variable $Y$ has a probability distribution. It is germane to study how this probability distribution of $Y$ changes as the level of $X$ changes.