A polling company conducts an annual poll of adults about political opinions. Th

Question

A polling company conducts an annual poll of adults about political opinions. The survey asked a random sample of 406 adults whether they think things in the country are going in the right direction or in the wrong direction. 45% said that things were going in the wrong direction. Complete parts a and b below. Calculate the margin of error for the proportion of all adults who think things are going in the wrong direction for 90% confidence. Would the margin of error be larger or smaller for 85% confidence? Explain.

Explanation / Answer

ME = Z0.05 × sd/n

= 1.96 × (0.45 ×0.55/406)

= 1.96 × 0.025 = 0.048

b.) A. To be less confident , the interval needs to contain the true proportion less often,so the margin of error would be smaller

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