Final answer:
The lower bound of the 90% confidence interval is not provided, but would be part of an interval such as (67.18, 68.82). The confidence interval suggests a range likely to contain the population mean with a given confidence, and the width of the interval is affected by the chosen confidence level.
Step-by-step explanation:
The question involves constructing a 90% confidence interval for the mean hours studied by students.
The confidence interval is an estimate used to infer the population mean from sample data.
The lower bound of the 90% confidence interval that was provided is not specified in your question, so I cannot provide the exact number.
However, if the confidence interval were (67.18, 68.82), the lower bound would be 67.18.
When we talk about confidence intervals, it's important to recognize that they are ranges of values that are believed to contain the actual population parameter with a certain level of confidence.
For example, if we were to construct 100 of these intervals, we would expect that 90 of them would contain the true population mean (statistics exam score in the context).
Changing the confidence level affects the error bound and the width of the interval. For instance, increasing the confidence level to 95% from 90% would result in a wider interval because we require more certainty that our interval includes the true population mean.
Conversely, decreasing the confidence level would result in a narrower interval with a smaller error bound, but less certainty of containing the true mean.