The data below is taken from two random, independent samples. Cal...

10. Hypothesis Testing for Two Samples

Two Proportions

Statistics

10. Hypothesis Testing for Two Samples

Two Proportions

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Multiple Choice

The data below is taken from two random, independent samples. Calculate the margin of error for a 99% confidence interval for the difference in population proportions.
$x sub 1 equals 87$ , $x sub 2 equals 68$
$n sub 1 equals 120$ , $n sub 2 equals 115$

0.061

0.062

0.158

0.060

Verified step by step guidance

Step 1: Understand the problem. We are tasked with calculating the margin of error for a 99% confidence interval for the difference in population proportions. The given data includes the sample successes (x₁ = 87, x₂ = 68) and sample sizes (n₁ = 120, n₂ = 115).

Step 2: Calculate the sample proportions for each group. The sample proportion for group 1 is p̂₁ = x₁ / n₁, and for group 2, it is p̂₂ = x₂ / n₂. Use these formulas to compute the sample proportions.

Step 3: Compute the standard error (SE) for the difference in proportions. The formula for SE is: SE = sqrt((p̂₁(1 - p̂₁) / n₁) + (p̂₂(1 - p̂₂) / n₂)). Substitute the values of p̂₁, p̂₂, n₁, and n₂ into this formula.

Step 4: Determine the critical value (z*) for a 99% confidence level. For a 99% confidence interval, the z* value corresponds to the 99% level of confidence, which is approximately 2.576. This value is derived from the standard normal distribution.

Step 5: Calculate the margin of error (ME). The formula for ME is: ME = z* × SE. Multiply the critical value (z*) by the standard error (SE) to find the margin of error.

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The data below is taken from two random, independent samples. Calculate the margin of error for a 99% confidence interval for the difference in population proportions.x1=87x_1=87, x2=68x_2=68n1=120n_1=120, n2=115n_2=115

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The data below is taken from two random, independent samples. Calculate the margin of error for a 99% confidence interval for the difference in population proportions.
$x sub 1 equals 87$ , $x sub 2 equals 68$
$n sub 1 equals 120$ , $n sub 2 equals 115$