APFIVE Pooled Proportion Calculation Error
When comparing two proportions, a researcher pools data from two groups to calculate the pooled proportion $$p_c$$. Instead of computing $$p_c = \frac{x_1+x_2}{n_1+n_2}$$ correctly, she makes an error in the calculation. What mistake did she commit?
TABLE: Two-Sample Data for Pooled Proportion
| Group | Successes | Sample Size |
|---|---|---|
| Group 1 | 84 | 125 |
| Group 2 | 72 | 150 |
A
She confused the pooled proportion with the individual sample proportions.
B
She misapplied the normal approximation due to a small sample size.
C
She incorrectly computed the pooled proportion, leading to an erroneous standard error.
D
She should not have pooled the proportions since the samples are independent.
E
She incorrectly set the significance level, affecting the pooled standard error calculation.
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