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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?

The weights in pounds of 23 dogs were used to construct the following stem-and-leaf display using the first digit as the stem and the second digit as the leaf:. Stem     Leaves                                                    3            2     4 4            0     3     4     5     7     8     9 5            0     1     2     3     4     5 6            1     2     5     6     7 7            0     1 8 9            8 Use the stem-and-leaf display to find the upper quartile.

An animal scientist is interested in determining the proportion of ewes (i.e., female sheep) that give birth to twins.  Rather than examine the records for all ewes in the United States, the animal scientist randomly selects 500 ewes and finds that 220 of them gave birth to twins. Construct a 99% confidence interval to estimate the true population proportion of ewes, p, who give birth to twins.  Interpret the meaning of this confidence interval.

The mean grade on an Organic Chemistry exam is a 50 and the standard deviation of the grades is 10.  The highest grade in the class was a 95.  Calculate the z-score for the student with the highest score of 95.  Based in the z-score, is this grade of 95 an outlier?  Why or why not?

Suppose that 80% of the Holstein cows in the U.S. give birth to their calves with no calving difficulty.  We randomly select 7 Holstein cows from the population consisting of all Holstein cows in the U.S.  What is the probability that at least 5 of the 7 (i.e., 5 or more) cows in this sample will give birth to their calves with no calving difficulty?  To find the answer to this question, you can use the equation for the binomial distribution or a binomial probability table.