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Answer:
95% confidence interval for the proportion of the adults who were opposed to the death penalty is (0.668, 0.704).
Step-by-step explanation:
We are given that a survey asked whether respondents favored or opposed the death penalty for people convicted of murder. Software shows the results below, where X refers to the number of the respondents who were in favor.
X = 1,790
N = 2,610
= Sample proportion = X/N = 0.6858
Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;
P.Q. = ~ N(0,1)
where, = sample proportion = 0.6858
n = sample of respondents = 2,610
p = population proportion
<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% level of significance 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> = [ ,
]
= [ ,
]
= [0.668 , 0.704]
Therefore, 95% confidence interval for the population proportion of the adults is (0.668, 0.704).