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an economist reports that 700 out of a sample of 2,800 middle-income american households actively participate in the stock market. construct the 90% confidence interval for the proportion of middle-income americans who actively participate in the stock market. note: round final answers to 3 decimal places.

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we are 90% confident that the true proportion of middle-income Americans who actively participate in the stock market lies somewhere between 23.7% and 26.3%.

to construct the 90% confidence interval for the proportion of middle-income Americans who actively participate in the stock market:

1. Calculate the sample proportion:

sample proportion (p) = number of successes / sample size

p = 700 / 2,800 = 0.25

2. Calculate the standard error:

standard error (SE) = √(p * (1-p) / sample size)

SE = √(0.25 * (1-0.25) / 2,800) = 0.008

3. Find the z-score for a 90% confidence level:

For a 90% confidence level, the z-score is 1.645.

4. Calculate the confidence interval:

lower bound = p - z-score * SE

lower bound = 0.25 - 1.645 * 0.008 = 0.237

upper bound = p + z-score * SE

upper bound = 0.25 + 1.645 * 0.008 ≈ 0.263

5. Round the final answers:

Therefore, the 90% confidence interval for the proportion of middle-income Americans who actively participate in the stock market is approximately 0.237 to 0.263

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