Social networking is becoming more and more popular among school-going teenagers

Question

Social networking is becoming more and more popular among school-going teenagers. Camden Research Group used a survey of students in several states to determine the percentage of students who use social networking sites. Assume that the results for surveys in Georgia, Maryland, Washington, and Wyoming are as follows.

Answer the following 6 questions.

1. We wish to conduct a hypothesis test to determine whether the proportion of students using social networking sites are equal for all four states. What is the value of your test statistic?

2. True or False: At least one state's population proportion is different from the others. (5% significance)

3. What is the sample proportion for Georgia?

4. Which state has the largest sample proportion?

5. Using the multiple comparison procedures, answer the following:

True or False: There is a significant difference between Georgia and Maryland. (5% significance)

6. Using the multiple comparison procedures, answer the following:

True or False: There is a significant difference between Wyoming and Maryland. (5% significance)

States Use Social
Networking Sites Georgia
Maryland
Washington Wyoming Yes 344 265 301 500 No 456 235 399 500

Explanation / Answer

1)

test statisitic = 20.473

2)

p-value = 0.00135 < 0.05

we reject the null hypothesis

true

3)

344/800 = 0.43

4)

Maryland is correct

as p > 0.5 in this case only

c1 c2 c3 c4 sum r1 344 265 301 500 1410 r2 456 235 399 500 1590 sum 800 500 700 1000 3000 Eij 1 2 3 4 expected 1 376 235 329 470 2 424 265 371 530 0i 344 265 301 500 456 235 399 500 Ei 376 235 329 470 424 265 371 530 sum (Oi-Ei)^2/Ei 2.723404 3.829787 2.382979 1.914894 2.415094 3.396226 2.113208 1.698113 20.47371 p-value 0.000135 critical value 7.82

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