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A severe drought has affected several western states in recent years.  A Christmas tree farmer is worried about the drought’s effect on the size of his trees.  To determine whether the growth of his trees has been reduced by the drought, the farmer decides to take a sample of the heights of 6 trees and obtains the following results (recorded in inches): Tree Height 1 60 2 57 3 62 4 69 5 46 6 54 Find the variance of the heights of this sample of 6 trees.

Finnish Landrace ewes are noted for producing “litters” of lambs. The number of lambs in a litter for a sample of 6 Finnish Landrace ewes is as follows:  Ewe Number           Number of Lambs in Litter        1                                        3        2                                        4        3                                        3        4                                        2        5                                        5        6                                        4   Calculate the standard deviation of litter size.

Suppose we have a population of horses with a mean weight of 1,000 lb and a standard deviation of 50 lb.  If we were to take repeated random samples of size n = 100 from the population, the mean and standard deviation, respectively, of the sampling distribution of the sample mean would be:

The weaning weights of 3 herds of beef cattle are compared across the 4 seasons of the year.  Thus, this is a 3 x 4 factorial experiment with 3 herds and 4 seasons.  Three calves from each herd are sampled during each season (i.e., there are 3 replications).  The resulting data were analyzed using Analysis of Variance and the partially completed ANOVA table is as follows: Source              df            F            Total                  35 Herd                   2         17.2 Season               3          3.0 Herd x Season    6          1.2 Error                  24                              Was there a significant difference among the 3 herd means for weaning weight?  Use a significance level of α = 0.05.

A local consumer reporter wants to compare the average cost of grocery items purchased at 3 different supermarkets:  Kroger, Giant Eagle, and Sam’s Club.  Prices (in dollars) were recorded for a sample of 10 randomly selected grocery items at each of the 3 supermarkets (i.e., a total of 10 x 3 = 30 prices were recorded).  We will consider this to be a one-way analysis of variance (i.e., a completely randomized design).  The partially completed Analysis of Variance table is shown below: Source               df          SS          MS          F        Total                               120 Supermarkets                  20 Error                               100                                          List the total degrees of freedom, the degrees of freedom for treatments (i.e., for supermarkets), and the error degrees of freedom.

The Analysis of Variance for a randomized block design produced the partially completed ANOVA table shown below. Source             df          SS            MS            F  Total                 24      131.3 Treatments        3        28.2 Blocks               5         69.0 Error                16        34.1                                  Find the mean squares for treatments, blocks, and error.

Health care issues are receiving a greal deal of attention in both the academic and political arenas.  A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance.  The ages (in years) of 8 uninsured senior citizens were as follows: Senior Citizen Age 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79     Find the median age of these 8 senior citizens.

The birth weights in pounds of 7 calves were as follows: Calf Weight 1 68 2 70 3 64 4 90 5 74 6 72 7 87         Find the median birth weight of these 7 calves.

It seems reasonable to assume that the number of times a team punts the ball in a football game would be negatively correlated with the number of points that the team scores (i.e., if a team is forced to punt frequently they are probably not moving the ball very well and probably are not scoring many points).  Number of punts (variable X) and number of points scored (variable Y) for a particular team in a random sample of five games are as follows: Number of Punts, X          Number of Points, Y              2                                         35              5                                         14              3                                         21              2                                         21              2                                         28   Calculate the covariance between variables X and Y.

A two-factor factorial experiment is conducted to compare litter sizes of Yorkshire and Landrace sows derived either from a line unselected for litter size or from a line that has gone through 15 years of selection for increased litter size.  Two sows of each breed are randomly selected from each line.  Their litter sizes are as follows:                                   Yorkshire       Landrace            Unselected line               8                     9                                        9                    10 Selected line                 11                    11                                      10                      9                                                                                     The partially completed ANOVA table is as follows:  Source             df             SS                MS            F  Total                              7.875 Line                               3.125            3.125       3.57 Breed Line x Breed Error                              3.500            0.875                                                                                       Find the calculated F value for breed.