Blog

The owner of a herd of cows wants to determine the influence of the ages of his cows on the amount of calving difficulty that occurs in his herd.  He constructs the following table:                             Age of Cow (in years)                                           0-2     3-5     6-10     over 10   Total No difficulty     40      35       20          5            100 Difficult birth   35      45       15          5            100 Total                  75      80       35        10           200   Given that the randomly selected cow had no difficulty in giving birth to her calf, what is the probability that she was more than than 2 yr old?

The weights (in pounds) of a sample of 6 dogs are as follows: Dog Weight 1 30 2 32 3 26 4 42 5 40 6 46 Find the mean of the weights of this sample of 6 dogs.

A box plot can be used to detect outliers in a dataset.  Assume that we have derived the following values for a dataset: lower outer fence = 169 lb       lower inner fence = 197.5 lb lower quartile = 226 lb             upper quartile = 245 lb upper inner fence = 273.5 lb   upper outer fence = 302 lb   The two lightest weights in the dataset are 160 lb and 165 lb.  The two heaviest weights in the dataset are 280 lb and 285 lb.  Based on a box plot, which one of the following statements is correct?

Which one of the following is not an assumption for the randomized block design?

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.