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. Country Use Social Great United Networking Sites Britain Israel 265 235 Russia 301 399 States 344 500 No 456 500 a. Conduct a hypothesis test to determine whether the proportion of adults using social networking sites equal for all four countries. Using a .05 level of significance. Use Table 12.4 Choose correct answer from above cholce H a All population proportions are equal The p-value is less than .01 What is your conclusion? Conclude the population proportions are not all equal.

Answer 1

Claim: The proportion of adults using social networking sites equal for all four countries.

The null and alternative hypothesis are:

Chi-square test of homogeneity of proportion is applicable

Test statistics:

The formula of chi square test statistics is

Where O - Observed frequencies

E - Expected frequencies

The observed frequencies of four countries using social networking sites are 344, 265, 301 and 500

There are 4 countries so the proportion of each country is 1/4

Total frequency = 344 + 265 + 301 + 500 = 1410

Expected frequency = n * p = 1410 * (1/4) = 352.5

Degrees of freedom = number of categories(countries) - 1 = 4 - 1 = 3

By using excel

Conclusion:

Reject the null hypothesis since P value is less than alpha (0.05)

Reject the null hypothesis, that is at least one proportion differs.