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A two-factor factorial experiment is conducted to compare litter sizes of Yorkshire and Landrace sows derived either from a line unselected for litter size or from a line that has gone through 15 years of selection for increased litter size.  Two sows of each breed are randomly selected from each line.  Their litter sizes are as follows:                                   Yorkshire       Landrace            Unselected line               8                     9                                        9                    10 Selected line                 11                    11                                      10                      9                                                                                     The partially completed ANOVA table is as follows:  Source             df             SS                MS            F  Total                              7.875 Line                               3.125            3.125       3.57 Breed Line x Breed Error                              3.500            0.875                                                                                       What is the correct conclusion regarding the line x breed interaction?  Use a significance level of 0.05.

Suppose that a 95% confidence interval for μ turns out to be (100 lb, 500 lb).  To make more useful inferences from the data, it is desired to reduce the width of the confidence interval.  What action should we take to reduce the width of the confidence interval?

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:

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets – Kroger, Giant Eagle, and Meier.  Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets.  In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item                          Kroger    Giant Eagle    Meier     1) Big Thirst Towel      $1.21       $1.49          $1.59 2) Post Golden Crisp    2.78         2.99            3.35 3) Tylenol Tablets         5.98         5.29            5.98           .                              .              .                   .           .                              .              .                   . 59) Colgate Shave       0.94         1.10            1.19 60) Kidney Beans        0.45          0.56            0.38                                                                                   The results of the Analysis of Variance for this experiment are as follows: Source           df       SS            MS          F     Total                       222.21     Supermarket              2.64       1.32       39.23 Item                        215.59       3.65     108.54 Error                           3.97      0.0337                                                                                What is the correct value of the test statistic for determining whether the three supermarkets have the same average prices?

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?

If the difference between the mean levels of factor A is independent of the levels of factor B, then there is ____________ between factors A and B.

Find the probability of an observation lying more than z = 2.25 standard deviations below the mean.

The weaning weights of two breeds of beef cattle are compared in two different regions of the US (say Florida and Wyoming).  When the mean weaning weights of the two breeds in the two different states are graphed, the lines are not parallel, and, in fact, intersect with each other.  What do you conclude?

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).

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).