Question

A magazine reports that women trust recommendations from a particular social networking site more than recommendations from any other social network platform. But does trust in this social networking site differ by gender? The following sample data show the number of women and men who stated in a recent sample that they trust recommendations made on this particular social networking site.

Women - Men

Sample - 150 - 170

Trust Recommendations - 123 - 85

Made on the social networking site

(a) What is the point estimate of the proportion of women who trust recommendations made on this particular social networking site?

(b) What is the point estimate of the proportion of men who trust recommendations made on this particular social networking site?

(c) Provide a 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on this particular social networking site. (Round your answers to four decimal places.)

Answer 1

Solution:

Sample proportion is the point estimate of population proportion.

a) Sample proportion of women who trust recommendations made on this particular social networking site will be the point estimate of the proportion of women who trust recommendations made on this particular social networking site.

Hence, point estimate of the proportion of women who trust recommendations made on this particular social networking site is,

b) Sample proportion of men who trust recommendations made on this particular social networking site will be the point estimate of the proportion of men who trust recommendations made on this particular social networking site.

Hence, point estimate of the proportion of men who trust recommendations made on this particular social networking site is,

c) The 95% confidence interval estimate of the difference between the two population proportions is given by,

Where,   

n_{​​​​​​1} and n_{​​​​​​2} are sample sizes. Z_(0.05/2) is critical z-value to construct 95% confidence interval.

We have,

Using Z-table we get, Z_(0.05/2) = 1.96

Hence, 95% confidence interval is,

The 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on this particular social networking site is (0.2153, 0.4247).