(a) A poll of 2,256 likely voters was conducted on the president’s performance. Approximately what margin of error would the approval rating estimate have if the confidence level is 95%? (Round your answer to 4 decimal places.)  Margin of error    ___________      (b) The poll showed that 46 percent approved the president’s performance. Construct a 90 percent confidence interval for the true proportion. (Round your answers to 4 decimal places.)  The 90% confidence interval is from ________  to  ___________   (c) Would you agree that the percentage of all voters opposed is likely to be 50 percent?  Yes, the confidence interval contains .50.No, the confidence interval does not contain .50.

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Asked Sep 29, 2019
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(a) A poll of 2,256 likely voters was conducted on the president’s performance. Approximately what margin of error would the approval rating estimate have if the confidence level is 95%? (Round your answer to 4 decimal places.)
  
Margin of error    ___________     
 
(b) The poll showed that 46 percent approved the president’s performance. Construct a 90 percent confidence interval for the true proportion. (Round your answers to 4 decimal places.)
  
The 90% confidence interval is from ________  to  ___________  
 
(c) Would you agree that the percentage of all voters opposed is likely to be 50 percent?
  

  • Yes, the confidence interval contains .50.
  • No, the confidence interval does not contain .50.
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Expert Answer

Step 1

(a) Total number of voters, n is 2256. Consider the population proportion, p as 0.5. The confidence level is 95%. Therefore, the level of significance is 1 – confidence level = 5% or 0.05.

The margin of error is,

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P(1-p) E = vn Foos 0.5(1-0.5) 0.05 2256 Z0.0250.5(1-0.5) 2256 1.96 0.5(1-0.5) 2256 (Using standard nomal table) 0.0206

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Step 2

(b) The sample proportion is provided as 0.46. The confidence level is 90%. Therefore, the level of significance is 1 – confidence level = 10% or 0.10.

The margin of error is,

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p(1-p) E F0.100.46(1-046 2256 F0s0.46(1-0.46 2256 1.650.46(1-0.46) (Using standard nomal table) 2256 0.0173

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Step 3

The 90% confidence interval for...

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CI. ptE 0.46t 0.0173 (0.4427,0.4773)

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