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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)
where, = 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
P( <
<
) = 0.95
P( < p <
) = 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].