Final answer:
The correct answer would be 'a) The sample size is not influenced by prior estimates.'
Step-by-step explanation:
The question "A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained for a 95% confidence interval if he does not use any prior estimates?" pertains to determining the appropriate sample size for statistical estimation when no prior estimates are available. When the researcher has no prior estimate of the population proportion, it is common to use 0.5 as the estimate for the proportion since this provides the maximum variance and hence, the largest sample size would be calculated. This is a conservative approach to ensure sufficient sample size for the desired confidence level.
The formula for calculating the required sample size without prior estimates, when wanting a 95% confidence interval, is:
n = (Z^2 * p * (1 - p)) / E^2
Where:
Z is the z-value (1.96 for 95% confidence),
p is the estimated proportion of the population (0.5 when no prior information is available),
E is the desired margin of error.
The sample size is not significantly influenced by prior estimates, so the correct answer would be 'a) The sample size is not influenced by prior estimates.' However, actual practice often dictates that researchers will seek any available prior information as it could impact the efficiency and practicality of the survey design.