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Independent random samples of litter sizes were selected from the Yorkshire and Landrace breeds of swine with the following results: Yorkshire          Landrace 8 pigs                    7 pigs 9                            8 10                          9 8                            8 9                            7 10                               54                        39  The correction factor (correction for the mean) in this problem is 786.27272. Calculate the Total Sums of Squares.

Assume X is a binomial random variable.  If n = 20 and p = 0.20, find P (r = 2 successes).

A random sample of 16 Standardbred horses was selected from a population of Standardbreds.  The mean time required for these 16 horses to run a mile while pulling a sulky was 130 seconds (i.e., 2 minutes and 10 seconds),  The standard deviation of the sample was 10 seconds. What is the point estimate of the true population mean for racing time of Standardbred horses?

A vet clinic has found that the number of patients per day has an average of 100 and a standard deviation of 10.  If nothing is known about the shape of the distribution of number of patients seen per day, what percentage of the days would be expected to have between 70 and 130 patients?

A 2 x 4 factorial experiment is conducted to compare yields of 4 varieties of soybeans that are planted in rows either 15 inches or 30 inches apart.  Two plots of ground are randomly assigned to each combination of soybean variety and row spacing.  The yields of soybeans (in bushels per acre) are as follows:           Rows 1 2 3 4 15″ 45 46 47 46   46 46 48 43 30″ 35 41 42 39   32 39 38 41 The partially completed ANOVA table is as follows: Source df SS MS F Total   319.75     Variety   41.25 13.75 5.0 Row spacing   225 225 81.8 Variety x row spacing   31.5     Error   22 2.75   Calculate the mean squares and then the F value for the variety x row spacing interaction.

Find the mean of a binomial probability distribution with a sample size of n = 40 and a probability of success of 0.60.

Suppose that X has a binomial probability distribution with n = 15 and p = 0.70.  Use the normal approximation to the binomial to calculate P(X>9).

Which one of the following is not an assumption when we perform an Analysis of Variance?

A randomized block design yielded the following Analysis of Variance table:       Source             df        SS                MS                F Total                 14      836       Treatments        4       501       125.25 Blocks                2       225       112.50 Error                  8       110          13.75                      Find the critical F value from the F tables that should be used to compare to the calculated F value for treatments.  Assume that we will use a significance level (α) of 0.05.

Assume that the probability that a calf will be red in color is 0.25 and the probability that the calf will have horns is 0.50.  Coat color and the presence or absence of horns are independent events.  What is the probability that the calf will be red and will have horns?