Provide a complete solution with all work shown.

A rural county hospital offers several health services. The hospital administrators conducted a poll to determine whether the residents' satisfaction with the available services depends on their gender. A random sample of 1,000 adult county residents was selected. The gender of each respondent was recorded and each was asked whether he or she was satisfied with the services offered by the hospital. The resulting data are shown in the table below.

384	416	800
80	120	200
464	536	1,000

a. Using a significance level of 0.05, conduct an appropriate test to determine if, for adult residents of this county, there is an association between gender and whether or not they were satisfied with services offered by the hospital.

b. Isa reasonable estimate for the proportion of all adult county residents who are satisfied with the services offered by their hospital? Explain why or why not.