We want to estimate the proportion (p) of cows conceiving at first service in an AI program on a particular farm.  How many cows would need to be included in the sample if it was desired to estimate p correct to within 0.05 with probability equal to 0.90?  Assume that we have a prior estimate of p which is equal to 0.60.

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             Do the data provide sufficient evidence to indicate that the treatment means differ?  Use α = 0.05.

A random sample of 4,000 U.S. citizens was asked their opinion concerning gun control.  A total of 2,600 of the 4,000 citizens in the sample stated that they are in favor of gun control legislation.  Perform the calculations needed to determine whether or not it would be appropriate to construct a large-sample confidence interval for the true population proportion (p).  What do you conclude (i.e., is it appropriate) and why?

We want to test the hypothesis that the mean weight of a breed of dogs is greater than 40 lb.  Therefore, we obtain the weights of a random sample of 36 dogs. The dogs in the sample weighed an average of 43 lb with a standard deviation of 6 lb.  We want to test:    Ho:  μ = 40 lb    Ha:  μ > 40 lb using a significance level (α) = 0.05. Should we reject Ho:  μ = 40 lb?  Explain.

A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a school levy in a certain school distruct.  A random sample of 400 people of voting age is selected.  Results of the poll show that 240 of the 400 people polled plan to vote in favor of the school levy.  What is the point estimate of the true population proportion of people who plan to vote in favor of the school levy?

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). Should we reject or not reject the null hypothesis that the mean frame scores of these two breeds are equal?

A two-factor factorial experiment is conducted to compare fleece weights of Merino, Suffolk, and Dorset ewes fed one of two diets.  Two ewes of each breed are randomly assigned to each diet.  The fleece weights (in pounds) are as follows:                Merino            Suffolk            Dorset        Diet 1          14                   9                    8                     15                 10                    8 Diet 2           13                   8                  11                     12                    9                 12                                                                                   The partially completed ANOVA table is as follows: Source             df           SS             MS           F      Total                          66.2500 Diet                             0.0833       0.0833       0.19992 Breed                        46.5000     23.2500     55.79955 Diet x Breed              17.1667     Error                            2.5000      0.41667                                                                                       The correct values for the diet x breed mean squares and F value, respectively, are:

Find the standard deviation of a binomial probability distribution with a sample size of n = 25 and a probability of success of 0.30.

Assume we are given the following information for yields of corn (in bushels per acre):    Median = 150     Lower quartile = 130     Upper quartile = 170    Lowest yield = 80     Highest yield = 250 Construct a box plot for these data.  Based on this box plot, is the largest yield of 250 bushels per acre a suspect or highly suspect outlier?

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 variance of the final grades in the math class (i.e., variable X).