Final answer:
To create a 90% confidence interval for the mean number of minutes used for recreational sites on library computers, sample data is needed. With this, calculate the sample mean, standard deviation, standard error, and obtain the critical t-value. Use these to establish the interval's bounds, remembering that factors unaccounted for in the margin of error might affect the interval.
Step-by-step explanation:
To make a 90% confidence interval for the mean number of minutes the library's computers are used each day for looking at recreational sites, we need to follow a statistical process. The steps below assume that we have the necessary data to perform the calculation.
- Firstly, obtain the sample data for the number of minutes the library’s computers are used for recreational sites per day.
- Calculate the sample mean (point estimate) and sample standard deviation.
- Determine the sample size (n).
- Since this is likely a small sample size or we lack population variance, use the t-distribution to find the critical t-value for a 90% confidence interval. This requires knowing the degrees of freedom, which is n - 1.
- Calculate the standard error by dividing the sample standard deviation by the square root of the sample size.
- Multiply the critical t-value by the standard error to determine the margin of error.
- Add and subtract this margin of error from the sample mean to get the lower and upper bounds of the confidence interval.
If the survey or sampling methodology has potential biases or errors, such as selection bias, non-response bias, or measurement errors, these wouldn't be accounted for in the margin of error and could impact the confidence interval. The factors like the time of day, demographics of the library users, and specific library policies could also affect the amount of time spent on recreational sites.
Regarding the change in the confidence interval with different confidence levels - as the confidence level decreases, the confidence interval would get narrower since you are less confident about the range in which the true mean lies.