Using sample statistics and the data from Problem 3.10 construct a 95% confidence interval:

(a) for a single observation, and identify any observations that may be identified as possible outliers.

(b) for the population variance.

Problem 3.10

The following data represent 60 planimeter observations of the area within a plotted traverse.

1.677 1.676 1.657 1.667 1.673 1.671 1.673 1.670 1.675 1.664 1.664 1.668 1.664 1.651 1.663 1.665 1.670 1.671 1.651 1.665 1.667 1.662 1.660 1.667 1.660 1.667 1.667 1.652 1.664 1.690 1.649 1.671 1.675 1.653 1.654 1.665 1.668 1.658 1.657 1.690 1.666 1.671 1.664 1.685 1.667 1.655 1.679 1.682 1.662 1.672 1.667 1.667 1.663 1.670 1.667 1.669 1.671 1.660 1.683 1.663

(a) Calculate the mean and standard deviation.

(b) Plot the relative frequency histogram (of residuals) for the data above using a class interval of one-half of the standard deviation.

(c) Calculate the E50 and E90 intervals.

(d) Can any observations be rejected at a 99% level of certainty?

(e) What is the peak value for the normal distribution curve, and where are the points of inflection on the curve?