Answer:
95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].
Step-by-step explanation:
We are given that in a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football.
Firstly, the pivotal quantity for 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is given by;
         P.Q. =  ~ N(0,1)
 ~ N(0,1)
where,  = proportion of adults in the United States whose favorite sport to watch is football in a sample of 1219 adults =
 = proportion of adults in the United States whose favorite sport to watch is football in a sample of 1219 adults = 
            n = sample of US adults  = 1291
            p = population proportion of adults 
<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>
So, 95% confidence interval for the population proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% 
                                                     significance level are -1.96 & 1.96}
P(-1.96 <  < 1.96) = 0.95
 < 1.96) = 0.95
P(  <
 <  <
 <  ) = 0.95
 ) = 0.95
P(  < p <
 < p <  ) = 0.95
 ) = 0.95
<u>95% confidence interval for p</u> = [  ,
 ,  ]
 ]
                          = [  ,
 ,  ]
 ]
                          = [0.265 , 0.316]
Therefore, 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].