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 407 adults whether they think things in the country are going in the right direction or in the wrong direction. 44% 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. ME-(Round to three decimal places as needed.) b) Would the margin of error be larger or smaller for 80% confidence? Explain. O A. To be less confident, the interval needs to contain the true proportion more often, so the margin O B. To be less confident, the interval needs to contain the true proportion less often, so the margin of of error would be larger. error would be smaller. of error would be smaller. O D. To be less confident, the interval needs to contain the true proportion less often, so the margin of error would be larger.

Explanation / Answer

Data given is:

n = 407, p = 0.44

Margin of error for a 95% CI is calculated using the formula: 1.96*S

Here, S = standard error = (p*(1-p)/n)^0.5 = (0.44*(1-0.44)/407)^0.5 = 0.0246

The 80% CI is narrower than 95% CI, so the margin of error will also be smaller.

To be less confident, the interval needs to contain the true population more often so the margin of error would be smaller.

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