1. In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately (a) 0.0094 (b) 0.0306 (c) 0.0353 (d) 0.2500 (e) 6.1237

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1. In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately (a) 0.0094 (b) 0.0306 (c) 0.0353 (d) 0.2500 (e) 6.1237

Answer 1

### (b) 0.0306

Answer 2

## Step 1: Identify the formula for the standard error of the sample proportion The standard error (SE) of a sample proportion \( p \) is calculated using the formula: \[ SE = \sqrt{\frac{p(1-p)}{n}} \] Where \( p \) is the sample proportion and \( n \) is the sample size. ## Step 2: Substitute the given values into the formula Given that \( p = 0.25 \) and \( n = 200 \), substitute these values into the formula: \[ SE = \sqrt{\frac{0.25 \cdot (1-0.25)}{200}} \] ## Step 3: Simplify the expression Calculate the numerator: \[ 0.25 \cdot (1-0.25) = 0.25 \cdot 0.75 = 0.1875 \] Next, divide by the sample size \( n \): \[ \frac{0.1875}{200} = 0.0009375 \] ## Step 4: Calculate the square root Find the square root of the result to get the standard error: \[ SE = \sqrt{0.0009375} \approx 0.0306 \]

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1. In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately (a) 0.0094 (b) 0.0306 (c) 0.0353 (d) 0.2500 (e) 6.1237

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