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?

Question

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

Answer 1

@John I have come from a year later to reply to your concern, to uproot this tyranny that is Math Guru. No longer shall we sit wondering what the other half of the question is. No longer must we be given a formula and have to solve it out. NO LONGER MUST WE SIT THROUGH THIS.

The answer is E.

Answer 2

Standard error = √(p1(1-p1)/n1 + p2(1-p2)/n2)

Your data:
n1 = 384
n2 = 432
p1 = 112/384
p2 = 91/432

If you substitute the data into the formula above, you should find standard error to be .0303, which will narrow down your choices. I'll let you determine the pooled value for p.

Answer 3

@MathGuru you're useless. You only solve the obvious and then leave us hanging.

Answer 4

I got only love for John. The answer is fate

Answer 5

@Robert Thank you o wise one

Answer 6

In order to find the pooled value for p̂ (the pooled proportion) and the pooled standard error of the difference between the two sample proportions, we need to use the formulas for calculating these values.

1. Pooled value for p̂:
The pooled value for p̂ is calculated by combining the proportions from both samples. We can use the formula:
p̂ = (x1 + x2) / (n1 + n2)
where x1 and x2 are the number of individuals who work at more than one job in each sample, and n1 and n2 are the respective sample sizes.

For Dalto City:
x1 = 112 (the number of individuals who work at more than one job in the first sample)
n1 = 384 (the sample size of the first sample)

For East Dettweiler:
x2 = 91 (the number of individuals who work at more than one job in the second sample)
n2 = 432 (the sample size of the second sample)

Therefore, the pooled value for p̂ is:
p̂ = (112 + 91) / (384 + 432) = 203 / 816 = 0.249

2. Pooled standard error of the difference between the two sample proportions:
The pooled standard error of the difference is calculated using the formula:
SE = sqrt((p̂ * (1 - p̂) / n1) + (p̂ * (1 - p̂) / n2))
where p̂ is the pooled proportion and n1 and n2 are the respective sample sizes.

Using the same values as before:
p̂ = 0.249
n1 = 384
n2 = 432

Substituting these values into the formula:
SE = sqrt((0.249 * (1 - 0.249) / 384) + (0.249 * (1 - 0.249) / 432))
SE = sqrt(0.000036 + 0.000031)
SE = sqrt(0.000067)
SE ≈ 0.0082

So, the pooled value for p̂ is 0.249, and the pooled standard error of the difference between the two sample proportions is approximately 0.0082.

Therefore, the correct answer is: .249, .017