Final answer:
The population mean for university admissions exam test scores is estimated to be between 61 and 69.07 with a 95% confidence interval. The width of the interval is 8.07 points, which reflects the level of certainty (95%) that the interval contains the true population mean. A 90% confidence interval would be narrower since it reflects less certainty.
Step-by-step explanation:
The question asks about calculating a confidence interval for the population mean of university admissions exam test scores using a given sample standard deviation and sample size. A 95% confidence interval indicates there is a 95% probability that the interval from 61 to 69.07 contains the true population mean. This interval has a range of 69.07 - 61 = 8.07 points.
When discussing confidence intervals, we refer to the certainty with which we expect the interval to contain the population mean. For example, a 90% confidence interval will be narrower, as it requires less certainty than a 95% confidence interval. If the question were about a 90% interval, we would expect that to be slightly smaller than the one mentioned in the question.
Understanding the Central Limit Theorem and the empirical rule is crucial for interpreting these intervals, as they give us important rules about the distribution of sample means around the population mean, especially as the sample size grows.