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.

An egg wholesaler wants to compare four methods of shipping eggs to determine which method results in the fewest broken eggs.  Five lots of eggs are shipped using each of the four methods.  The number of broken eggs in each lot is recorded and shown in the table below.  The wholesaler wants to determine if the average number of broken eggs is the same for each shipping method.  Therefore, he tests the null hypotheses using a 0.01 significance level. Shipping Method Sample lot no. A B C D 1 4 9 1 9 2 3 7 6 7 3 1 6 4 7 4 2 8 3 6 5 5 8 4 8 Total 15 38 18 37 Mean 3.0 7.6 3.6 7.4 What is the degrees of freedom for total, treatment, and error in the Analysis of Variance table?

The ages (in years) of a sample of 6 students are as follows: Student Age 1 19 2 23 3 20 4 20 5 19 6 19                 Calculate the standard deviation of this sample of 6 student ages.

An animal scientist is interested in determining the proportion of ewes that give birth to twins.  Rather than examine the records for all ewes in the United States, he randomly selects 500 ewes and finds that 220 of them gave birth to twins.  Construct a 99% large-sample confidence interval to estimate the true population proportion of ewes who give birth to twins.

The person in charge of genetic evaluation of beef cattle wants to know if birth weights of calves are influenced by breed and if they are influenced by the region of the U.S. (i.e., Northern U.S. vs Southern U.S.) in which the calf is born.  She has heard that calves born in the South are usually lighter at birth than are calves born in the North.  In order to answer these questions, she sets up a 2 x 3 factorial experiment with 3 replications and obtains the birth weights (in pounds) shown in the following table:                   Angus       Charolais       Simmental North             85                93                 91                       85                92                 92                       83                94                 92   South            85                84                  82                      76                85                   83                      74                83                   83       The partially completed ANOVA table is as follows: Source               df             SS            MS          F       Total                                 548.00 Location Breed                               174.33       87.165     13.643 Location x breed                  9.00         4.500 Error                                                                                         Find the degrees of freedom for total, location, breed, location x breed, and error, respectively.

An Animal Scientist wants to estimate the average weaning weight of the Angus breed of beef cattle.  Therefore, he selects a random sample of 100 Angus calves and weighs them on the day they are weaned from their mothers.  The sample mean for these 100 calves is 500 lb and the sample standard deviation is 40 lb.  Which one of the following is the correct 90% confidence interval used to estimate the population mean for the weaning weights of the Angus calves?

Assume X is a binomial random variable.  If n = 5 and p = 0.10, find P (r > 1 success).

An egg wholesaler wants to compare four methods of shipping eggs to determine which method results in the fewest broken eggs.  Five lots of eggs are shipped using each of the four methods.  The number of broken eggs in each lot is recorded and shown in the table below.  The wholesaler wants to determine if the average number of broken eggs is the same for each shipping method.  Therefore, he tests the null hypotheses using a 0.01 significance level. Shipping Method Sample lot no. A B C D 1 4 9 1 9 2 3 7 6 7 3 1 6 4 7 4 2 8 3 6 5 5 8 4 8 Total 15 38 18 37 Mean 3.0 7.6 3.6 7.4 What is the calculated value of the F statistic in the Analysis of Variance table given that the total SS = 122.8, treatment SS = 89.2, and error SS = 33.6?

A beef cattle nutritionist wants to compare the birth weights of calves from cows that receive two different diets during gestation.  He therefore selects 10 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 = 11 lb Standard deviation of the difference in birth weights of the pairs = 6.53 lb Which one of the following is the correct 95% confidence interval for the true mean difference in birth weights of the calves from cows receiving diet 1 vs. diet 2?

Health care issues are receiving a greal deal of attention in both the academic and political arenas.  A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance.  The ages (in years) of 8 uninsured senior citizens were as follows: Senior Citizen Age 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79     Calculate the mean age of these 8 senior citizens.