Suppose You Want to Estimate the Difference Between Two Population $0.03$

question 91

Multiple Choice

Suppose you want to estimate the difference between two population proportions correct to within $0.03$ with probability $0.90$ . If prior information suggests that $\mathrm { p } _ { 1 } \approx 0.4$ and $\mathrm { p } _ { 2 } \approx 0.8$ , and you want to select independent random samples of equal size from the populations, how large should the sample sizes be?

• A) \(n _ { 1 } = n _ { 2 } = 1708\)
• B) \(\mathrm { n } _ { 1 } = \mathrm { n } _ { 2 } = 963\)
• C) \(\mathrm { n } _ { 1 } = \mathrm { n } _ { 2 } = 1925\)
• D) \(\mathrm { n } _ { 1 } = \mathrm { n } _ { 2 } = 1203\)

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Definitions:

Self-Serving Bias

A common tendency for individuals to attribute their successes to personal characteristics and their failures to external factors.

Self-Effacing Bias

The tendency to downplay one's own success or attribute positive outcomes to external factors rather than to one's own efforts or abilities.

Rationalization Attribution

The process of explaining an individual's behavior with logical, but not always true, reasons to justify actions or opinions.

Self-Serving Bias

The common human tendency to attribute success to personal characteristics and failures to external factors, thereby protecting self-esteem.