Question

# A polling company conducts an annual poll of adults about political opinions. The survey asked a...

A polling company conducts an annual poll of adults about political opinions. The survey asked a random sample of 2354 adults whether they think things in the country are going in the right direction or in the wrong direction. 62​% said that things were going in the wrong direction. Complete parts a and b below.

​a) Calculate the margin of error for the proportion of all adults who think things are going in the wrong direction for 95​% confidence.

Solution :

Given that,

n = 2354

Point estimate = sample proportion = =62%=0.62

1 -   = 1- 0.62=0.38

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2   * ((( * (1 - )) / n)

= 1.96 (((0.62*0.32) /2354 )

E = 0.018

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