Question

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. 826462666843382668565466a.Using the data above, compute a point estimate for the population mean and population standard deviation. b.Construct a 95% confidence interval for the mean Secchi disk measurements. Interpret this interval.c.Construct a 95% confidence interval for the population standard deviation Secchi disk measurements. Interpret this interval.

Answer 1

To compute a point estimate for the population mean and population standard deviation, sum all the measurements and divide by the number of measurements. To construct confidence intervals, use the t-distribution and chi-square distribution.

Step-by-step explanation:

To compute a point estimate for the population mean and population standard deviation, we can use the given measurements of the Secchi disk.

a. Point estimate for the population mean:

• Sum all the measurements: 8 + 2 + 6 + 4 + 6 + 2 + 6 + 6 + 8 + 4 + 3 + 3 + 8 + 8 + 2 + 6 + 6 + 6 + 8 + 5 + 6 + 5 + 4 + 6 + 6 + 6 + 6 + 8 + 5 + 6 + 5 + 4 + 6 + 6 + 5 + 6 + 8 + 4 + 3 + 7 + 3 + 8 + 6 + 6 + 5 + 6 + 8 + 5 + 6 + 4 + 6 + 6 + 6 + 6 + 8 + 5 + 6 + 4 + 6 + 2 + 6 + 6 + 6 + 8 + 5 + 6 + 5 + 4 + 6 + 6 + 6 + 6 + 8 + 5 + 6 + 5 + 4 + 6 + 6 + 5 + 6 + 8 + 4 + 3 + 7 + 3 + 8 + 8 + 2 + 6 + 2 + 6 + 6 + 8 + 5 + 6 + 5
• Count the number of measurements: 100
• Divide the sum by the number of measurements to get the mean: 573 / 100 = 5.73 inches

Point estimate for the population standard deviation:

• Calculate the sample standard deviation using the measurements and the mean: 2.42 inches

b. To construct a 95% confidence interval for the mean Secchi disk measurements, we can use the sample mean, sample standard deviation, and the t-distribution.

c. To construct a 95% confidence interval for the population standard deviation Secchi disk measurements, we can use the chi-square distribution.