Question

Social networking is becoming more and more popular around the world. Pew Research Center used a survey of adults in several countries to determine the percentage of adults who use social networking sites (USA Today, February 8, 2012). Assume that the results for surveys in Great Britain, Israel, Russia, and United States are as follows

use social network?	UK	Israel	Russia	USA
Yes	344	265	301	500
No	456	235	399	500

a. State the null and alternative hypotheses and conduct a test to determine whether the proportion of adults using social networking sites is equal for all four countries. What is the degrees of freedom? What is the p‐value? Using a 5% level of significance, what is your conclusion?

b. What are the sample proportions for each of the four countries? Which country has the largest proportion of adults using social networking sites? Using a 5% level of significance, conduct multiple comparison tests among the four countries. What is your conclusion? What is the degrees of freedom?

Answer 1

(a) The hypothesis being tested is:

H0: The proportion of adults using social networking sites is equal for all four countries

Ha: The proportion of adults using social networking sites is not equal for all four countries

		UK	Israel	Russia	USA	Total
Yes	Observed	344	265	301	500	1410
	Expected	376.00	235.00	329.00	470.00	1410.00
	O - E	-32.00	30.00	-28.00	30.00	0.00
	(O - E)² / E	2.72	3.83	2.38	1.91	10.85
No	Observed	456	235	399	500	1590
	Expected	424.00	265.00	371.00	530.00	1590.00
	O - E	32.00	-30.00	28.00	-30.00	0.00
	(O - E)² / E	2.42	3.40	2.11	1.70	9.62
Total	Observed	800	500	700	1000	3000
	Expected	800.00	500.00	700.00	1000.00	3000.00
	O - E	0.00	0.00	0.00	0.00	0.00
	(O - E)² / E	5.14	7.23	4.50	3.61	20.47
		20.47	chi-square
		3	df
		.0001	p-value

The p‐value is 0.0001.

The degrees of freedom is 3.

Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the proportion of adults using social networking sites is not equal for all four countries.

(b) The sample proportions are:

		UK	Israel	Russia	USA	Total
Yes	Observed	344	265	301	500	1410
	% of total	0.11	0.09	0.10	0.17	0.47
No	Observed	456	235	399	500	1590
	% of total	0.15	0.08	0.13	0.17	0.53
Total	Observed	800	500	700	1000	3000
	% of total	0.27	0.17	0.23	0.33	1.00

The USA has the largest proportion of adults using social networking sites.

The degrees of freedom is 3.

There is a significant difference between the USA and Isreal.

There is a significant difference between the UK and Isreal.