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.