-10 - | 5 -12 | + 3 + | 5 + 12 | =
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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).
We can use the vertical angle theorem which states that any two opposite angles are congruent. So, you can just set the two measures equal to each other and solve for x:
So, your answer is 20°.
So, your answer is 20°.