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A telephone poll of 1000 adult Americans was reported in a magazine. One of the questions...

A telephone poll of 1000 adult Americans was reported in a magazine. One of the questions asked was "What is the main problem facing the country?" Suppose 28% answered "crime". We are interested in the population proportion of adult Americans who feel that crime is the main problem. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed.

Which distribution should you use for this problem? (Round your answers to three decimal place.)

  

Construct a 95% confidence interval for the population proportion of adult Americans who feel that crime is the main problem.

Sketch the graph

math   Statistics-And-Probability   
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Answer #1

n = 1000, p̅ = 0.28  

we should z-test distribution for this.

95% Confidence interval :  

At α = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/2) =    1.960

Lower Bound = p̄ - z_c*√( p̄ *(1- p̄ )/n) = 0.28 - 1.96 *√(0.28*0.72/1000) =    0.252

Upper Bound = p̄ + z_c*√( p̄ *(1- p̄ )/n) = 0.28 + 1.96 *√(0.28*0.72/1000) =    0.308

0.252 < p < 0.308  

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