College-Educated or Not? 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 in Table 5.2.

(a) What proportion of college graduates answered yes when asked if they had ever used online dating? What proportion of those with a high school degree or less said yes? What is the sample difference in proportions?

(b) Use the fact that the standard error for the estimate is 0.019 to find a \(99 \%\) confidence interval for the population difference in proportions.

(c) Is it plausible that there is no difference between college graduates and high school graduates or less in how likely they are to use online dating? Use the confidence interval from part (b) to answer, and explain your reasoning.

Refer to Data 5.2, which describes a survey conducted in July 2015 asking a random sample of American adults whether they had ever used online dating (either an online dating site or a dating app on their cell phone).

Data 5.2:
A survey conducted in July 2015 asked a random sample of n = 2001 American adults whether they had ever used online dating (either an online dating site or a dating app on their cell phone). Overall, 15% said that they had used online dating, showing an increase over the percentage in a similar survey conducted two years earlier. (Two groups in particular showed a change over this two-year period: Usage by 18- to 24-year-olds nearly tripled while usage by 55- to 64-yearolds more than doubled.)

Table 5.2 Have you ever used an online dating site or a dating app?

\begin{array}{l|cc|r}
\hline & College & High School & Total \\
\hline Yes & 157 & 70 & 227 \\
No & 666 & 565 & 1231 \\
\hline Total & 823 & 635 & 1458 \\
\hline
\end{array}