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In a study regarding public opinion about a national policy, a random sample of 40 people showed that 25 agreed with the policy: How many more people should be included in the sample to be 95% sure that the sample estimate is within four percentage points of the population proportion, p?

User Kobie
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Final answer:

To be 95% confident that the sample estimate is within four percentage points of the population proportion, an additional 560 people should be included in the sample.

Step-by-step explanation:

To determine the number of people that need to be included in the sample to be 95% confident that the sample estimate is within four percentage points of the population proportion, we can use the formula for sample size calculation:

n = (Z^2 * p * (1-p)) / E^2

Where:

  • n is the required sample size
  • Z is the Z-score (corresponding to the desired confidence level)
  • p is the estimated population proportion
  • E is the desired margin of error

In this case, we already have a sample of 40 people and the proportion who agree with the policy is 25/40 = 0.625. We want to be 95% confident and have a margin of error of 0.04. The Z-score for a 95% confidence level is approximately 1.96. By substituting these values into the formula, we can solve for n:

n = (1.96^2 * 0.625 * (1-0.625)) / 0.04^2 = 600

Therefore, to be 95% confident that the sample estimate is within four percentage points of the population proportion, an additional 560 people should be included in the sample.

User Hobgoblin
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