Question

The survey also asked participants for their level of education, and we wish to estimate the difference in the proportion to use
online dating between those with a college degree and those with a high school degree or less. The results are shown in the
two-way table below.
College High School Total
Yes 157 70 227
No 666 565 1231
Total 823 635 1458

Let group 1 be the proportion of college graduates using online dating and group 2 be the
proportion of high school graduates using online dating.

Is it plausible that there is no difference between college graduates and high school graduates in
how likely they are to use online dating? Use the confidence interval from part above to answer.

Answer 1

Solution:-

The 95% confidence interval for the difference in the proportion is C.I = ( 0.0431, 0.1181).

$C.I = \left (p_{1}-p_{2} \right )\pm z_{\alpha /2}\times \sqrt{\frac{p_{1}(1-p_{1})}{n_{1}}+\frac{p_{2}(1-p_{2})}{n_{2}}}$

C.I = (0.1908 - 0.11023) + 1.96*0.01915

C.I = 0.0806 + 0.0375

C.I = ( 0.0431, 0.1181)

Since the 95% confidence interval for the difference in the proportion contains all the positive values, hence it is not plausible that there is no difference between college graduates and high school graduates in how likely they are to use online dating.