Frame score in beef cattle is based on height at the hips and is used as a measure of skeletal size.  Frame scores range from 1 to 10 with a higher number indicating a taller animal.  Independent random samples of frame scores were selected from the Angus and Simmental breeds of beef cattle with the following results: Angus Simmental 5 7 6 7 7 8 5 6 7 7 6   Using the appropriate table, find the critical F value needed to test the null hypothesis that the breed means for frame score are equal (use α = 0.05).

A randomized block design was used to compare the mean responses for three treatments.  Four blocks of three homogeneous experimental units were selected, and each treatment was randomly assigned to one experimental unit within each block.  The partially completed ANOVA table for this experiment is as follows: Source               df        SS             MS          F   Total                  11       84.489 Treatments         2       12.032       6.016 Blocks                3       71.749      23.916 Error                  6         0.708        0.118             Calculate the F value for treatments and for blocks.

Assume that 20% of all pigs die between birth and weaning.  In a random sample of 200 births, let X be the number of pigs that die between birth and weaning.  Using the normal approximation to the binomial, find the approximate probability that the number of pigs in the sample of 200 that die between birth and weaning is greater than or equal to 50.

An experiment results in one of two possible outcomes, A or B.  We know that P(A) = 0.40, P(B) = 0.60, and P(A ∩ B) = 0.20.  Find the P(A U B).

The owner of a herd of pigs wants to determine if the weights of any of her pigs are outliers.  The average weight of the pigs in her herd is 250 lb and the standard deviation of the weights is 50 lb.  The heaviest pig weighs 275 lb.  What should the owner of the pigs conclude?

A beef cattle nutritionist wants to compare the birth weights of calves from cows that receive two different diets during gestation.  He therefore selects 16 pairs of cows, where the cows within each pair have similar characteristics.  One cow within each pair is randomly assigned to diet 1, while the other cow in the pair is assigned to diet 2.  He obtains the following results:      Mean difference in birth weights of the pairs of calves = 10 lb      Standard deviation of the difference in birth weights of the pairs = 8.0 lb Construct a 95% confidence interval for the true mean difference in birth weights of the calves from cows receiving diet 1 vs. diet 2.

Assume X is a binomial random variable.  If n = 10 and p = 0.40, find P (r = 2 successes).

We are interested in estimating the average driving time of students who commute to Ohio State.  How many students who commute need to be included in our sample to order to be 98% confident that the estimated mean driving time will be within 4 minutes of the true population mean driving time if the standard deviation of the driving times is 8 minutes?

The  ∑  symbol in a statistical equation indicates that we are to perform which arithmetic operation?

A study was conducted to determine whether a student’s final grade in a high school math class is linearly related to his or her performance on the math ability test administered before college entrance.  The math test scores and final grades for a random sample of 10 students are shown below. Final Grade in Math Class (X)          Math Ability Test Score (Y) 65                                                             39 78                                                             43 52                                                             21 82                                                             64 92                                                             57 89                                                             47 73                                                             28 98                                                             75 56                                                             34 75                                                             52 Find the covariance between the final grades in the math class (i.e., variable X) and the math ability test scores (i.e, variable Y).