A professor in the Department of Animal Sciences wants to estimate the mean weight of the Suffolk breed of lambs shown at the Ohio State Fair in the past five years.  Therefore, he selects a random sample of n = 25 lamb weights and obtains a sample mean of 125 lb and a sample standard deviation of 15 lb.  Construct a 95% confidence interval for the true population mean of the weights of Suffolk lambs shown at the Ohio State Fair in the past five years.

The mean length of time required to complete a 5K race was 20 minutes.  The standard deviation of the times was 4 minutes.  The racing times were approximately normally distributed.  What proportion of the runners would be expected to require between 18 and 25 minutes to complete the race?

Independent random samples of litter sizes were selected from the Yorkshire and Landrace breeds of swine with the following results: Yorkshire          Landrace 8 pigs                    7 pigs 9                            8 10                          9 8                            8 9                            7 10                               54                        39  The correction factor (correction for the mean) in this problem is 786.27272. Calculate the Treatment (i.e., breed) Sums of Squares.

Finnish Landrace ewes are noted for producing “litters” of lambs. The number of lambs in a litter for a sample of 6 Finnish Landrace ewes is as follows:  Ewe Number           Number of Lambs in Litter        1                                        3        2                                        4        3                                        3        4                                        2        5                                        5        6                                        4 What is the median litter size?

Find the area under the normal curve between z = -1.35 and z = 1.85.

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                                                                                         Calculate the sums of squares (SS) for location.

A plant breeder develops a new wheat variety she hopes will yield more in the plains than the three most popular varieties under dry-land farming conditions.  She sets up a randomized block experiment with the three major types of soil in the region – sand, clay, and loam – as the blocks.  She selects a field with each soil type, divides it into four sections, and randomly selects one of the four wheat varieties for planting in each section.  The yields in bushels per acre in each section are shown in the following table. Variety Block A B C D Total Sand 20 21 21 18 80 Clay 25 24 21 20 90 Loam 30 28 22 20 100 Total 75 73 64 58 270 The correction factor for this Analysis of Variance is 6,075 and the total sums of squares is 141. What is the correct conclusion regarding soil types (i.e., blocks) in this randomized block experiment?  Use a significance level of 0.05.

An industrial psychologist is investigating the effects of work environment on employee attitudes.  A group of 20 recently hired sales trainees were randomly assigned to one of 4 different “home rooms” with 5 trainees per room.  Each room was identical except for the color of the walls.  The 4 colors used were light green, light blue, gray, and red.  Therefore, in this experiment the 4 treatments were the 4 room colors.  The psychologist wants to compare the mean attitudes of the trainees assigned to the 4 rooms with different colors.  At the end of the training program, the attitude of each trainee was measured on a 60 point scale (the lower the score, the poorer the attitude).  The data were subjected to an analysis of variance.  The partially completed Analysis of Variance (ANOVA) table was as follows: Source           df       SS              MS              F     Total                       1,829.75 Treatments             1,678.15 Error                          151.60                                      Calculate the F value.  Based on a significance level of α = 0.05, the F value from Table IX in the back of our textbook is 3.24.  What should the industrial psychologist who conducted this experiment conclude?  Explain.

A randomized block design is used to compare litter sizes of the Yorkshire and Duroc breeds of sows.  Blocking is used in an attempt to remove the effects of sow age, since it is known that sow age influences litter size.  Each block contains sows of similar ages.  The data collected for this experiment are as follows:                   Yorkshire       Duroc       Block totals Block 1          9 pigs         7 pigs         16 pigs Block 2         10                8                18 Block 3         11                9                 20 Block 4         13              10                 23                                                                             Totals           43              34                 77   The partially completed ANOVA table for this experiment is as follows:   Source          df          SS          MS          F        Total                        23.875 Breed                      10.125      10.125      81.0 Block                       13.375       Error                          0.375                                   Calculate the mean square for blocks and the mean square for error and then calculate the F statistic for blocks.

The weights of 25 lambs (in pounds) in a flock of sheep are as follows: 68     73     66     76     86     74     61     89     65     90 69     92     76     62     81     63     68     81     70     73     60     87     75     64     82 Construct a stem-and-leaf display using the first digit as the stem and the second digit as the leaf.  Based on the stem-and-leaf display, the upper quartile for this set of weights is __________ lb.