Testing of Hypothesis

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

Contingency Tables | Cross Classification: Introduction

Contingency Tables also called cross tables or two-way frequency tables describe 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 $Y$ be two categorical response variables. Let variable $X$ have $I$ levels and variable $Y$ have $J$. 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.

Contingency Tables, Cross Tabulation

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.

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MCQs Hypothesis Statistics 6

Online MCQs Hypothesis Statistics 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. Let us start with the Online MCQs Hypothesis Statistics Quiz.

MCQs Hypothesis Testing

1. Fisher exact test is used for:

 
 
 
 

2. When a critical region is located on both sides of the curve, it is called

 
 
 
 

3. The choice of a one-tailed test and a two-tailed test depends upon

 
 
 
 

4. The level of significance is the risk of

 
 
 
 

5. In a Wilcoxon rank sum test

 
 
 
 

6. If $\alpha=0.05$%, the value of one-tailed $Z$ test will be

 
 
 
 

7. Which of the following is (are) considered to be inferential statistics?

 
 
 
 

8. Which one is an example of a two-tailed test

 
 
 
 

9. The region of acceptance of $H_0$ is called

 
 
 
 

10. Type-I error will occur if an innocent person is

 
 
 
 

11. A .05 level of significance means that

 
 
 
 

12. The probability of rejecting a false $H_0$ is

 
 
 
 

13. If population standard deviation is known and $n>30$ then appropriate test statistics mean comparison is

 
 
 
 

14. A deserving player is not selected for the national team, it is an example of

 
 
 
 

15. Which of the following statistics can be used to determine whether or not there is a statistically significant relationship between two variables in a contingency table?

 
 
 
 

16. The region of rejection of $H_0$ is called

 
 
 
 

17. The probability of rejecting a true hypothesis is called

 
 
 
 

18. In a Z-test, the number of degrees of freedom is

 
 
 
 

19. A statistic on the basis of which a decision is made about the hypothesis of interest is called

 
 
 

20. A ________ error is made if $H_1$ is true but $H_0$ is accepted

 
 
 
 


Most of the MCQs on this page are covered from Estimate and Estimation, Testing of Hypothesis, Parametric and Non-Parametric tests, etc.

Step by Step Procedure of Hypothesis Statistics

Online MCQs Hypothesis Statistics

  • Type-I error will occur if an innocent person is
  • A deserving player is not selected for the national team, it is an example of
  • A __ error is made if $H_1$ is true but $H_0$ is accepted
  • A statistic on the basis of which a decision is made about the hypothesis of interest is called
  • The probability of rejecting a true hypothesis is called
  • The probability of rejecting a false $H_0$ is
  • The level of significance is the risk of
  • When a critical region is located on both sides of the curve, it is called
  • The choice of a one-tailed test and a two-tailed test depends upon
  • Which one is an example of a two-tailed test
  • The region of acceptance of $H_0$ is called
  • The region of rejection of $H_0$ is called
  • In a Z-test, the number of degrees of freedom is
  • If $\alpha=0.05$%, the value of one-tailed $Z$ test will be
  • If population standard deviation is known and $n>30$ then appropriate test statistics mean comparison is
  • In a Wilcoxon rank sum test
  • Fisher exact test is used for:
  • Which of the following statistics can be used to determine whether or not there is a statistically significant relationship between two variables in a contingency table?
  • Which of the following is (are) considered to be inferential statistics?
  • A .05 level of significance means that

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MCQs Hypothesis and Hypothesis Testing 5

Online MCQs Hypothesis and Hypothesis Testing 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. Let us start with the Online MCQs Hypothesis and Hypothesis Testing quiz.

Please go to MCQs Hypothesis and Hypothesis Testing 5 to view the test

Most of the MCQs on this page are covered from Estimate and Estimation, Testing of Hypotheses, Parametric and Non-Parametric tests, etc.

Hypothesis and Hypothesis Testing

MCQs Hypothesis and Hypothesis Testing Quiz

  • The first and starting point in hypothesis testing is
  • A hypothesis which is to be tested for the possible nullification is called
  • The hypothesis, which is being tested is
  • Which of the following can be $H_1$
  • Which of the following can be an alternative hypothesis $H_1$
  • A hypothesis in which all parameters are specified is called
  • If $H_0:\mu =10$ and $\sigma = 5$, then it is
  • Which one of the following cannot be a null hypothesis
  • The probability of type-I error is denoted by
  • The probability of rejecting $H_0$, when $H_0$ is true is called
  • Rejecting $H_0$ when $H_0$ is false is called
  • Rejecting $H_0$ when $H_0$ is true is called
  • A judge can release(acquit) a guilty person is an example of
  • A misfit person is not selected for a job is
  • A good scheme related to education is rejected by the education department, it is an example of
  • The greater the value of the F-ratio
  • If a hypothesis test were conducted using $\alpha=0.05$, for which of the following p-values, the null hypothesis be rejected:
  • To test $H_0:\sigma^2 = \sigma_o^2$, we use:
  • Nonparametric tests are used when the level of measurement is
  • The nonparametric equivalent of an unpaired samples t-test is the

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