The Animal Sciences Department wants to estimate the average length of time it takes students to complete a class project correct to within 5 hours with a 98% level of confidence.  Determine the sample size needed to estimate the average length of time required to complete the project to within 5 hours with a 98% level of confidence if the standard deviation of the times is 4 hours.

The average litter size in Ohio is approximately 8 pigs per litter.  Owners of a particular breed would like to prove that the mean litter size of their breed is greater than 8 pigs per litter.  Therefore, they want to test:      Ho:  μ = 8 pigs/litter      Ha:  μ > 8 pigs/litter They obtain a random sample of 100 litter size records from sows of this breed and find a sample mean of 8.4 pigs per litter and a sample standard deviation of 1 pig per litter.  They decide to use a significance level of α = 0.01. What is the correct conclusion?

The t and z distributions are very similar.  Both are symmetric, mound-shaped, and have a mean of zero.

Yearling weights of bull calves on a particular ranch are normally distributed with a mean of 1,200 lb and a standard deviation of 100 lb.  The owner of the ranch wants to keep the upper 10% of the bull calves based on weight in order to use them to breed his cows.  At what weight should the owner set the cutoff point if he wants to keep the upper 10% of the bull calves based on weight?

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.  Do the block means differ (i.e., was blocking effective in removing variation in litter size)?  Use a significance level of α = 0.05.

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 Y-intercept for the least squares regression line.

The FDA wants to compare the mean caffeine contents of two brands of cola, Brand A and Brand B.  In a preliminary study, a small number of independent random samples of cans of each brand were selected and the caffeine content of each can was determined.  The results were as follows:   Brand A Brand B Sample size 15 10 Mean (ounces) 18 20 Variance 1.2 1.5 How many cans of each brand of cola would need to be sampled in order to estimate the difference in poppulation mean caffeine contents to within 0.5 ounces with probability 0.95?

Weights of 40 dogs in a kennel are an example of what type of variable?

The Kimberly Clark Corporation wants to determine how many tissues a box of Kleenex should contain.  Researchers determine that 60 is the average number of tissues used by a typical person during a cold.  Suppose a random sample of 100 Kleenex users yielded a sample mean of 56 tissues and a sample standard deviation of 10 tissues used during a typical cold.  Kimberly Clark wants to test:    Ho:  μ = 60 tissues    Ha:  μ < 60 tissues using a significance level (α) = 0.05. What is the correct value of the test statistic that should be used to test the null hypothesis?

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 70 inches and a standard deviation of 10 inches. Estimate the population mean for length of horns of Longhorn cattle in Texas using a 90% confidence interval.  Explain the meaning of the confidence interval that you derived.