Carry out the steps in constructing a confidence interval for a population proportion: define the parameter; check conditions; perform calculations; interpret results in context.
A recent Gallup Poll conducted telephone interviews with a random sample of adults aged 18 and older. Data were obtained for 1000 people. Of these, 37% said that the football is their favorite sport to watch on television.
(a) Define the parameter p in this setting. Explain to someone who knows no statistics why we can't just say that 37% of all adults would say that football is their favorite sport to watch on television.
(b) Check conditions for constructing a confidence interval for p.
(c) Construct a 95% confidence interval for p.
(d) Interpret the interval in context.
Please show ALL of your work. The best answer with the most detail will be selected and awarded points.