EXAMPLE 8.11

Who uses Instagram? A recent study compared the proportions of young women and men who use Instagram.¹⁵ A total of 1069 young women and men were surveyed. These are the cases for the study. The response variable is User with values Yes and No. The explanatory variable is Sex with values “Men” and “Women.” Here are the data:

In this table, the column gives the sample proportions of women and men who use Instagram. The proportion for the total sample is given in the last entry in this column.

Let’s find a 95% confidence interval for the difference between the proportions of women and of men who use Instagram. We first find the difference in the proportions:

= 0.6108 − 0.4398

= 0.1710

Then we calculate the standard error of D:

= 0.0301

For 95% confidence, we have z* = 1.96, so the margin of error is

The 95% confidence interval is

D ± m = 0.1710 ± 0.0590

= (0.112, 0.230)

With 95% confidence, we can say that the difference in the proportions is between 0.112 and 0.230. Alternatively, we can report that the difference between the percent of women who are Instagram users and the percent of men who are Instagram users is 17.1%, with a 95% margin of error of 5.9%.