In a study, a random sample of 2625 US adults were asked whether they agree or disagree that there is "only one true love for each person." The response and gender of the participants is shown in Table 1. Male Female Total

Agree 372 363 735

Disagree 807 1005 1812

Don't know 34 44 78

Total 1213 1412 2625

Table 1 Is there only one true love for each person?

(a) Use the information in the table to construct a confidence interval for the difference in the proportion who agree, between males and females, using the fact that the standard error for the difference is .

Round your answers to three decimal places.

The 95% confidence interval is

to

.

(b) Is it plausible that there is no difference between males and females in the proportion who agree that each person has only one true love?