Final answer:
The student is referring to a statistical concept known as a 90% confidence level, meaning there's a 90% chance that the true mean falls within the constructed confidence interval. The margin of error is 3% of 69, which is roughly 2.07%. The confidence interval's purpose is to estimate the range wherein the actual mean likely falls.
Step-by-step explanation:
The claim that seniors will have an average score within 3% of 69% indicates the margin of error is 3% of 69, which is approximately equal to 2.07%. Since we're working with the statement that this occurs nine times out of ten, we're assuming a 90% confidence level. A confidence interval at this level would, theoretically, contain the population mean nine times out of ten if we were to repeat the sampling process many times.
Using the provided reference information, we estimate with 90 percent confidence that the true population mean exam score for all statistics students is between 67.18 and 68.82. If we were to construct 100 of these confidence intervals using different samples of students, we would expect that 90 of them would contain the true mean exam score for the entire population of seniors. This level of confidence helps us assess the reliability of our estimate.
The margin of error is the range on either side of the sample mean within which we expect the true population mean to fall. The confidence interval provides a range of values that plausibly includes the population mean. As the confidence level increases, say to 95 percent or 99 percent, the corresponding confidence interval becomes wider to accommodate the increased certainty that the interval includes the true mean.