The campus at Joliet Junior College has a lake. A student used a Secchi disk to measure the clarity of the lake’s water by lowering the disk into the water and measuring the distance below the water surface at which the disk is no longer visible. The following measurements (in inches) were taken on the lake at various points in time over the course of a year.
(a) Use the data to compute a point estimate for the population mean and population standard deviation.
(b) Because the sample size is small, we must verify that the data are normally distributed and do not contain any outliers. The figures show the normal probability plot and boxplot. Are the conditions for constructing a confidence interval about m satisfied?
(c) Construct a 95% confidence interval for the mean Secchi disk measurement. Interpret this interval.
(d) Construct a 99% confidence interval for the mean Secchi disk measurement. Interpret this interval.
(e) Construct a 95% confidence interval for the population standard deviation Secchi disk measurement. Interpret this interval.
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