A random sample of 384 people in Dalto City, a mid-sized city, revealed 112 individuals who work at more than one job. A second random sample of 432 workers from East Dettweiler, another mid-sized city, found 91 people who work at more than one job. To conduct a significance test for a difference in the proportions of workers in Dalto City and East Dettweiler who work at more than one job, what's the pooled value for p̂, and what's the pooled standard error of the difference between the two sample proportions, respectively?



.5, .0303

.249, .0009

.249, .017

.251, .0303

.249, .0303

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.249 .0303

To find the pooled value for p̂ (the pooled sample proportion), we need to calculate the weighted average of the sample proportions from each city. The formula for the pooled sample proportion is:

p̂ = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of individuals working at more than one job in each city, and n1 and n2 are the sample sizes for each city.

In this case, for Dalto City, x1 = 112 and n1 = 384, and for East Dettweiler, x2 = 91 and n2 = 432.

p̂ = (112 + 91) / (384 + 432)
p̂ = 203 / 816
p̂ ≈ 0.249

Therefore, the pooled value for p̂ is approximately 0.249.

To calculate the pooled standard error of the difference between the two sample proportions, we'll use the following formula:

SE = sqrt((p̂ * (1 - p̂) / n1) + (p̂ * (1 - p̂) / n2))

where p̂ is the pooled sample proportion and n1 and n2 are the sample sizes for each city.

In this case, p̂ ≈ 0.249, and the sample sizes are n1 = 384 and n2 = 432.

SE = sqrt((0.249 * (1 - 0.249) / 384) + (0.249 * (1 - 0.249) / 432))
SE ≈ sqrt(0.000647 + 0.000571)
SE ≈ sqrt(0.001218)
SE ≈ 0.0349

Therefore, the pooled standard error of the difference between the two sample proportions is approximately 0.0349.

So the correct answer is .249, .0349.