# Stating a confidence interval for odd ratio

A research institute surveyed 1000 online shoppers in the United States and China. One question asked if the online shopper followed brands they purchased through social media. Here are the results proportions:
The USA:    513/(513+487)=0.513, China: 928/(72+928) =0.928


I calculated the odd ratio as follows:

$$OR=(0.513/(1-0.513))/(0.928/(1-0.928))=1.053/12.889=0.0817$$

Then I constructed a 95% confidence interval for it (0.1377 was given as SE for $$b_1$$). Could I calculate it from data in the table above?

$$CI=-2.5043±1.96*0.1377=(-2.7742,-2.2344) \\ CIOR=(ex p⁡(-2.7742),exp⁡(-2.2344)=(0.062,0.107)$$

How can I sate this interval?

I wrote:

We are 95% confident that the U.S. online shoppers are as low as 0.062 and as high as 0.107 as likely to follow brands they purchased through social media as Chinese online shopper.

We are 95% confident that the odd ratio of the U.S. online shoppers who follow brands they purchased through social media vs. their Chinese counterparts is as low as 0.062 and as high as 0.107

Are they correct? I'm even afraid of their English grammar and meaning!

• Please tag with self-study tag Jun 14, 2019 at 14:16

$$se = \sqrt( 1 / 487 + 1 / 513 + 1 / 72 + 1 / 928)$$