It was reported that, in a sample of 565 adult Americans, only 162 correctly des
ID: 3150844 • Letter: I
Question
It was reported that, in a sample of 565 adult Americans, only 162 correctly described the Bill of Rights as the first ten amendments to the U.S. Constitution. Calculate a two-sided confidence interval using a 85 % confidence level for the proportion of all U.S. adults that could give a correct description of the Bill of Rights.
It was reported that, in a sample of 565 adult Americans, only 162 correctly described the Bill of Rights as the first ten amendments to the U.S. Constitution. Calculate a two-sided confidence interval using a 85 % confidence level for the proportion of all U.S. adults that could give a g:CDdyJ; f!YAYEjt.inn ci. ític, liill epi Kic3hi .. The critical value in the 85 % confidence interval for p is closest to Submit AnswerIncorrect. Tries 2/3 Previous Tries What is the standard error in the confidence interval for p? Submit Answer Tries 0/2 The lower limit of a two-sided 85 % confidence interval for p is closest to Submit Answer Tries 0/2 The upper limit of a two-sided 85 % confidence interval for p is closest to Submit Answer Tries 0/2Explanation / Answer
a.
crtical value = 1.44
b.
Standard Error = Sqrt(p*(1-p)/n))
x = Mean
n = Sample Size,
Mean(x)=162
Sample Size(n)=565
Sample proportion =0.287
Standard Error = Sqrt ( (0.287*0.713) /565) )
= 0.019
c & d.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=162
Sample Size(n)=565
Sample proportion = x/n =0.287
Confidence Interval = [ 0.287 ±Z a/2 ( Sqrt ( 0.287*0.713) /565)]
= [ 0.2867 - 1.44* Sqrt(0.0004) , 0.2867 + 1.44* Sqrt(0.0004) ]
= [ 0.26,0.314]
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