A random sample of 36 households was selected as part of a study on water usage in a small community, and the number of gallons was recorded for each household in the sample for the 2nd quarter of 2021. The data were approximately normally distributed with a mean of 450 gallons and a sample standard deviation of 90. A researcher intends to determine a 95% confidence interval for the population mean water usage during the period.

1. Will this confidence interval calculation be based on a z-interval or a t-interval? What is the rationale for that?
2. What is the point estimate for the confidence interval and how did you determine this?
3. Calculate the standard error SE. Show the calculations, using the data for this scenario.
4. A calculator gives the confidence interval as [419.55, 480.45]. What is that telling us? I.e., use that information in a sentence that summarizes these results.
5. Use an example to describe the relationship between sample size and standard error. I.e., as sample size increases or decreases, what happens to the standard error. Why is that?