A randomized block design is used to compare postweaning average daily gains of 4 breeds of beef cattle, Hereford, Angus, Charolais, and Simmental (we can think of the breeds at the “treatments”).  The breeds are divided into 3 weight classes (i.e., 3 blocks).  Block 1 contains cattle weighing 450 to 500 lb at the beginning of the experiment, block 2 contains cattle weighing 500 to 550 lb at the beginning of the experiment, and block 3 contains cattle weighing 550 to 600 lb at the beginning of the experiment.  The postweaning average daily gains (in pounds per day) are as follows:  Block Hereford Angus Charolais Simmental 1 3.50 3.60 3.70 3.75 2 3.55 3.63 3.71 3.80 3 3.56 3.62 3.80 3.90 The partially completed ANOVA table for this experiment is as follows: Source df SS MS F Total   .160     Breed   .139 .046 46 Block   .014 .007   Error   .007 .001   Calculate the F statistic for blocks.

Suppose that 10% of the Golden Retrievers in the U.S. have a particular genetic defect.  We randomly select 6 Golden Retrievers from the population consisting of all Golden Retrievers in the U.S.  What is the probability that at least one (i.e., one or more) of the 6 dogs in the sample will have the genetic defect?  To find the answer to this question, you may use either the binomial equation or you may use the attached binomial probability table.

Calculate the mean of the discrete probability distribution shown below:   X            2           4            5           10            P(X)       0.20       0.40       0.30       0.10  ____________________________________  

The mean of the starting salary data that we have been using is 28,475 dollars and the standard deviation is 9,369 dollars.  According to the Empirical Rule, we expect 99% of the starting salaries to fall between what two numbers?

The body weight in pounds (variable X) and fleece weight in pounds (variable Y) of a random sample of four ewes are as follows: Body weight, lb (X)            Fleece weight, lb (Y)           140                                            9           145                                          10           155                                          10           160                                          12                                                                                      Calculate the slope of the least squares line for the regression of Y (fleece weight) on X (body weight).

Assume X is a binomial random variable.  If n = 15 and p = 0.90, find P (r ≥ 10 successes).

We want to test the hypothesis that the mean number of credit hours taken per semester by OSU undergraduates is less than 16 hours.  Therefore, we obtain a random sample of credit hours for 49 students. The sample mean is 15 hours and the sample standard deviation is 4 hours.  We want to test:    Ho:  μ = 16 hours    Ha:  μ < 16 hours using a significance level (α) = 0.01. Should we reject or not reject the null hypothesis?  Why?

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.

Toyota would like to know how many miles per gallon the average person gets when driving the hybrid Toyota Prius.  A random sample of 225 drivers yields a mean of 50 mpg and a standard deviation of 7.5 mpg.  The point estimate of the population mean for the miles per gallon of the Toyota Prius would be:

The average height of a certain ornamental plant is 15 inches and the standard deviation of the heights is 3 inches.  Only 20% of the plants are expected to be more than X inches tall.  Find the value of X.