Final answer:
Given the conditions for constructing confidence intervals, the Sample size, success, failures, and population representation are crucial. Option D that states n×p×(1−p) > 10 is likely unsatisfied seems correct. A confidence interval approximates where a population parameter lies, with a certain degree of certainty based on the sample data.
Step-by-step explanation:
To determine whether the requirements for constructing a confidence interval about p are satisfied, we need to consider several conditions:
- The sample should be a simple random sample.
- The sample size should be no more than 5% of the population.
- The condition n×p×(1−p) should be greater than 10 to approximate a normal distribution.
- The number of successes np' and the number of failures nq' should both be greater than five.
Option D: No, the requirement that n×p×(1−p) is greater than 10 is not satisfied, seems to be the correct answer in this scenario based on the information provided that the binomial conditions aren't met (np and nq must both be greater than five.)
A confidence interval provides a range of values, within which there is a specified probability that the true parameter value lies. For example, a 90% confidence interval suggests that if we were to take many samples and construct the interval each time, about 90% of those intervals would contain the actual population mean.
Importance of Sample Size:
A larger sample size, say 500 campers as mentioned, will tend to produce a more precise confidence interval with a smaller error bound because it is more representative of the population.