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 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                                                                                       Find the calculated F value for breed.

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.

A scientist conducts an experiment to determine if the mean alkalinity level of water specimens from the Olentangy River is greater than 50 milligrams per liter (mpl).  She selects a random sample of 100 water specimens from the river and finds a sample mean of 67.8 mpl and a sample standard deviation of 14.4 mpl.  She decides to test the hypothesis using a significance level of 0.01.  Using this information, calculate the value of the test statistic.

Find the sample size needed to estimate the population proportion (p) correct to within 0.06 with probability 0.95.  Assume that we have previous information that indicates that p = 0.30.

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   Should we reject or not reject the null hypothesis for the interaction between variety and row spacing?  Use a significance level of α = 0.05.

The Environmental Science & Technology journal reported on a study of contaminated soil in The Netherlands.  A total of 81 soil specimens were sampled, dried, and analyzed for the contaminant cyanide.  The cyanide concentation (in milligrams per kilogram, mg/kg, of soil) of each soil specimen was determined using an infrared microscopic method.  The samples had a mean cyanide level of 95 mg/kg and a standard deviation of 50 mg/kg.  The authors of the journal article tested the hyothesis that the true mean cyanide level in the soil in The Netherlands was less than 100 mg/kg using a significance level of α = 0.10. Should the authors of the journal article reject the null hypothesis?  Explain.

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.

It is desired to test:      Ho:  p = 0.70      Ha:  p ≠ 0.70 A random sample of 50 cow records is chosen; 30 of these 50 cows conceived at first service.  Using a significance level of 0.01, which one of the following conclusions is correct?  You can assume that large-sample procedures are appropriate.

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                                                                                       Calculate the sums of squares for breed.