EXAMPLE 8.9 Social Media in the Supply Chain

CASE 8.3 Example 8.8 (page 438) analyzes data on the use of audio/visual sharing through social media by small and large companies. Are the proportions of social media users the same for the two types of companies? Here is the data summary:

The sample proportions are certainly quite different, but we need a significance test to verify that the difference is too large to easily result from the role of chance in choosing the sample. Formally, we compare the proportions of social media users in the two populations (small companies and large companies) by testing the hypotheses

The pooled estimate of the common value of is

This is just the proportion of label users in the entire sample.

First, we compute the standard error

and then we use this in the calculation of the test statistic

The difference in the sample proportions is almost five standard deviations away from zero. The -value is . In Table A, the largest entry we have is with . So, . Therefore, we can conclude that . Our report: 84% of small companies use audio/visual sharing through social media versus 52% of large companies; the difference is statistically significant .