Question

Assume that a sample is used to estimate a population proportion, p, for a U.S. President's job approval rating 2. Find the margin of error, aka Error Bound on the Proportion, EBP, that corresponds to a sample of size n=902 and a sample proportion of p′=55% that approve of the President's job performance, at a confidence level of 80%. EBP=% Answer should be obtained without any preliminary rounding. Round final answer to one tenth of one percent. Question Help: □ Video □ Message instructor Assume that a sample is used to estimate a population proportion, p, for a U.S. President's job approval rating 2. Find the margin of error, aka Error Bound on the Proportion, EBP, that corresponds to a sample of size n=902 and a sample proportion of p′=55% that approve of the President's job performance, at a confidence level of 80%. EBP=% Answer should be obtained without any preliminary rounding. Round final answer to one tenth of one percent. Question Help: □ Video □ Message instructor

Answer 1

To find the margin of error (Error Bound on the Proportion, EBP) for a sample of size n=902 with a sample proportion p′=55% at a confidence level of 80%, you can use the following formula:

EBP = Z * sqrt[(p' * (1 - p')) / n]

Where:

EBP is the margin of error.

Z is the critical value for the desired confidence level (in this case, 80%).

p' is the sample proportion.

n is the sample size.

First, find the critical value Z for an 80% confidence level. You can either use a Z-table or a calculator. For an 80% confidence level, Z is approximately 1.2816.

Now, plug in the values:

EBP = 1.2816 * sqrt[(0.55 * (1 - 0.55)) / 902]

Calculate the square root term:

sqrt[(0.55 * (1 - 0.55)) / 902] ≈ 0.0172 (rounded to four decimal places)

Now, calculate EBP:

EBP ≈ 1.2816 * 0.0172 ≈ 0.0221 (rounded to four decimal places)

Finally, convert EBP to a percentage:

EBP ≈ 2.21% (rounded to one-tenth of one percent)

So, the margin of error (Error Bound on the Proportion) at an 80% confidence level for a sample of size n=902 with a sample proportion p′=55% is approximately 2.21%.