Answer :
Complete Question
A polling agency conducted a survey about social media in which each person in random samples of 1,000 men and 1,000 women was asked what factor he or she considers to be the most important when deciding whether to connect on social media with another person. The responses are shown in the table
Factor
Personal Friend,Stay in Touch,Mutual Friends,Business Networking Other
Men 600 210 106 45 40
Women 650 224 65 15 46
What is the contribution to the chi square test statistic for men who selected business networking as the most important factor ?
a. 0.5
b. 5
c. 7.5
d. 30
e. 45
Answer:
Correct option is C
Step-by-step explanation:
From the question we are told that:
Sample
[tex]n =1,000 men+ 1,000 women[/tex]
Factor Table
Personal Friend,Stay in Touch,Mutual Friends,Business, Networking Other
Men 600 210 105 45 40
Women 650 224 65 15 46
Generally the equation for Expected value for Men, Business and networking X is mathematically given by
[tex]X= \frac{Row Total * Column Total}{Grand Total}[/tex]
[tex]X=\frac{(600 + 210 + 105 + 45 + 40)*(45 + 15)}{(600 + 210 + 105 + 45 + 40 + 650 + 224 + 65 + 15 + 46)}[/tex]
[tex]X=30.015[/tex]
Generally the equation for Chi Contribution is mathematically given by
[tex]Y= {(45 - 30.015)^2}{30.015}[/tex]
[tex]Y=7.48[/tex]
[tex]Y \approx 7.5[/tex]
Therefore
Correct option is C
The contribution to the chi square test statistic for men who selected business networking as the most important factor is 7.5
The expected value is calculated as:
[tex]X = \frac{RT * CT}{GT}[/tex]
Where:
RT represents the row total, CT represents the column total and GT represents the grand total.
For Men, Business and networking, we have:
[tex]X = \frac{(600+ 210 +105+45 + 40) * (45 + 15)}{(600 +210 +105 +45 +40 +650 +224 +65 +15 +46)}[/tex]
Evaluate the sum
[tex]X = \frac{1000 * 60}{2000}[/tex]
[tex]X = 30[/tex]
The contribution to the chi square test statistic for men who selected business networking is then calculated as:
Y = (Business Networking - X)^2 / X
This gives
[tex]Y = \frac{(45 - 30)^2}{30}[/tex]
Evaluate the difference
[tex]Y = \frac{15^2}{30}[/tex]
Evaluate the exponent
[tex]Y = \frac{225}{30}[/tex]
Evaluate the quotient
[tex]Y = 7.5[/tex]
Hence, the contribution to the chi square test statistic for men who selected business networking as the most important factor is 7.5
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