Lake Macatawa, an inlet lake on the east side of Lake Michigan, is divided into an east basin and a west basin. To measure the effect on the lake of salting city streets in the winter, scientists took 32 samples of water from the west basin and measure the amount of sodium in parts per thousand to make a statistical inference about the unknown mean. The obtained the following data:

13.0 18.5 25.2 15.6 16.4 14.8 23.1 17.6 19.4 17.3 15.3 23.2 24.9 19.4 20.8 19.3 16.0 18.8 23.1 21.7 15.2 19.9 15.2 19.1 18.1 21.3 25.1 16.8 21.5 20.4 17.4 16.8

b. Determine a 95% confidence interval for

c. Another type of estimation is a prediction interval, where the focus is on estimating the value of the next observation. Note that prediction intervals use thestandard deviations of the underlying distribution (not theof the sampling distribution). Assume that the measures for the random variable of sodium in the west basin are normally distributed, create two 95% prediction intervals: one using T distribution and one using a Z distribution . You may need to find a t/2with 31 degrees of freedom on the Internet. Since 32 is quite close to the n30, what are the differences in the intervals developed?

d. Suppose that there was another sample that had a measurement of 40.7 ppt and since it was outside the prediction intervals in part c., it is considered an outlier. If sodium levels are linked to harmful bacteria growth, what follow up or reporting changes would be performed due to this outlier? Suppose automated data collection and analysis in this area is a planned; what a procedure would be used for detecting and handling outliers?