Final answer:
A confidence interval is a range likely to contain the population parameter, with a certain degree of certainty. A 95% confidence interval means there's a 95% chance it contains the true population mean. A sample size increase leads to a smaller error bound, making the interval more precise.
Step-by-step explanation:
Describe the Confidence Interval
A confidence interval is a range of values that is likely to contain a population parameter with a certain level of confidence. In general, it means if we were to take many different samples and calculate a confidence interval from each of these samples, a specified percentage of these intervals would contain the true population parameter.
For this particular study, a 95% confidence interval means that we can be 95% confident that the interval contains the true mean score of the statistics exam.
Common Misconceptions
There is a common misconception that a 90% confidence interval will contain 90% of the data values. This is incorrect. Instead, it means if we were to take many samples and construct confidence intervals from these samples, about 90% of the intervals would capture the true population parameter.
Calculating Sample Size
To determine an appropriate sample size for a 95% confidence interval, we would need information such as the population proportion or variance, desired margin of error, and the z-score for our level of confidence. For a population proportion assumed to be 0.5 and a 95% confidence level within three percentage points of the population, the sample size calculation would take these values into account.
Effect on Error Bound and Confidence Interval
If the sample size increases to 500 campers, the error bound of the confidence interval is likely to decrease, making the interval more precise. This is because a larger sample size typically leads to a lower standard error.