Answer to Question #132159 in Statistics and Probability for Samir

Question

You are tasked with investigating whether fake news media platform and personality are independent. Consider the table below to help you with your task.

Celebrity .C/ Politician .P/ Sport Star .SS/ Total
Social Media .SM/ 1800 700 515 3015
Traditional Media .T M/ 485 350 150 985
Total 2285 1050 665 4000

Question 17
Which of the following statements is incorrect?
1. The expected frequency of Social Media and Politician is 791:44.
2. The expected frequency of Traditional Media and Sport Star is 163:76:
3. The observed frequency of Traditional Media and Politician is 350:
4. The null hypothesis is that Media platform and personality are dependent.
5. There are 2 degrees of freedom

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c} & C & P & SS & Total \\ \hline SM & 1800 & 700 & 515 & 3015 \\ \hdashline TM & 485 & 350 & 150 & 985 \\ \hdashline Total & 2285 & 1050 & 665 & 4000 \end{array}$$

$$E_{ij}=\dfrac{T_i\times T_j}{N}$$

1. $E_{12}=\dfrac{3015\times 1050}{4000}=791.4375\approx791.44$

The statement is correct.

2. $E_{23}=\dfrac{985\times 665}{4000}=163.75625\approx163.76$

The statement is correct.

3. $O=350$

The statement is correct.

4. The following null and alternative hypotheses need to be tested:

$H_0:$ The two variables are independent.

$H_1:$ The two variables are dependent.

This corresponds to a Chi-Square test of independence.

The statement is incorrect.

5. $df=(2-1)\times(3-1)=2$

The statement is correct.