Final answer:
The discussion is about creating confidence intervals for true proportions and means from survey data, emphasizing how the width changes with different confidence levels, and considering factors that might impact the survey's accuracy beyond the margin of error.
Step-by-step explanation:
The student's question pertains to the construction of confidence intervals for true proportions and means based on survey data. When creating a 99 percent confidence interval for the true proportion of a population, it involves determining the range within which we can say with high certainty that the true proportion lies, based on a given sample. For example, if a random sample of 25 statistics students includes six students who have used a product in the past week, the plus-four method can be used to estimate the true proportion of all statistics students who would report the same.
If we change the confidence level from 99 percent to 90 percent, the width of the confidence interval decreases. This means that the interval around the sample proportion or mean that is supposed to contain the true population proportion or mean becomes narrower because we are accepting a lower level of certainty. However, such a confidence interval will still contain the true value 90 percent of the time.
Confidence intervals can be affected by factors apart from the error mentioned (margin of error), such as the method of data collection, sample selection bias, and non-response bias. These cannot be accounted for by the margin of error and can impact the survey's accuracy.