Breeders of the Longhorn breed of cattle select to increase the length of the horns (i.e., the distance from the tip of one horn to the tip of the other horn).  A Longhorn breeder would like to know the average length of horns found on Longhorn cattle in Texas.  A random sample of 144 Longhorn cattle yields a mean horn length of 72 inches and a standard deviation of 15 inches. Estimate the population mean for length of horns of Longhorn cattle in Texas using a 95% confidence interval.

A study published in The Journal of American Academy of Business examined whether the perception of service quality at five-star hotels in Jamaica differs by gender.  In order to compare the means of two populations (i.e., male vs. female guests), independent random samples were selected from each population, with the results shown in the table below.  Use these data to construct a 96% confidence interval for the difference in the two population means.   Males Females Sample size 130 115 Sample mean score 39.10 38.70 Sample standard deviation 6.70 6.95

The manager of a swine operation wants to compare the litter sizes of three pigs of pigs – Duroc, Yorkshire, and Large White.  The manager obtains a random sample of litter sizes of sows of the three breeds as shown in the table below.  Use Analysis of Variance to test at the 0.05 significance level if there is a difference in the average litter sizes of the three breeds of pigs. Litter size Large White Duroc Yorkshire 10 6 11 6 7 8 8 9 13 12 4 10 6 6 10 10 12 5 6 8 6 Total 42 67 64 Average 8.4 6.7 10.7 What should the manager of the swine operation conclude regarding the average litter sizes of these three breeds of pigs?

A farm supply store manager wants to predict monthly sales, Y, for her company using advertising expenditures, X.  She has collected 10 months of data on past performance as shown in the following table. Advertising expenditures, in thousands of dollars, X Monthly sales, Y XY X2 Y2 1.2 101 121.2 1.44 10,201 0.8 92 73.6 0.64 8,464 1.0 110 110.0 1.00 12,100 1.3 120 156.0 1.69 14,400 0.7 90 63.0 0.49 8,100 0.8 82 65.6 0.64 6,724 1.0 93 93.0 1.00 8,649 0.6 75 45.0 0.36 5,625 0.9 91 81.9 0.81 8,281 1.1 105 115.5 1.21 11,025 TOTAL 9.4 959 924.8 9.28 93,569 Find the Y-intercept of the regression line for the regression of Y on X.

Breeders of the Longhorn breed of cattle select to increase the length of the horns (i.e., the distance from the tip of one horn to the tip of the other horn).  A Longhorn breeder would like to know the average length of horns found on Longhorn cattle in Texas.  A random sample of 144 Longhorn cattle yields a mean horn length of 72 inches and a standard deviation of 15 inches. Estimate the population mean for length of horns of Longhorn cattle in Texas using a point estimate.

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.