Use the following information for questions:
In a random sample of 250 full time students, 80% preferred to have three one-hour lectures per week rather than two 90-minute lectures. In a random sample of 500 part-time students, 50% said they preferred the three one-hour lectures schedule. The difference between the two sample proportions (full-time - part-time) is to be calculated.
-What is the standard error for the difference between the two sample proportions?
A) 0.0011
B) 0.0338
C) 0.0553
D) 0.6000

Question

Use the following information for questions:
 In a random sample of 250 full time students, 80% preferred to have three one-hour lectures per week rather than two 90-minute lectures. In a random sample of 500 part-time students, 50% said they preferred the three one-hour lectures schedule. The difference between the two sample proportions (full-time - part-time) is to be calculated.
-What is the standard error for the difference between the two sample proportions?
A) 0.0011
B) 0.0338
C) 0.0553
D) 0.6000

Quizplus · Accepted Answer

The standard error for the difference between two sample proportions is calculated using the formula: $\sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$, where $p_1$ and $p_2$ are the sample proportions, and $n_1$ and $n_2$ are the sample sizes. For full-time students, $p_1 = 0.80$ and $n_1 = 250$. For part-time students, $p_2 = 0.50$ and $n_2 = 500$. Plugging these values into the formula gives $\sqrt{\frac{0.80(0.20)}{250} + \frac{0.50(0.50)}{500}} = \sqrt{0.00064 + 0.0005} = \sqrt{0.00114} \approx 0.0338$.

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