A forester studying the effects of fertilization on certain pine forests in the Southeast is interested in estimating the average basal area of the pine trees. a. In studying basal areas of similar trees for many years, he has discovered that these measurements (in square inches) are normally distributed with standard deviation approx. 4 square inches. If the forester samples n = 9 trees, find the probability that the sample mean will be within 2 square inches of the population mean

b. Suppose now that the population standard deviation of basal areas is not known and must be estimated from the sample. If a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that Pr(g1<= (Y- μ )<= g2)=0.90

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above