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You are interested in purchasing a really good bull to breed your cows.  You look up the sale prices of a sample of 16 bulls that were sold in last year’s National Western Stock Show sale in Denver.  The average sale price was $10,000 with a standard deviation of $1,000.  Estimate the population mean for the sale prices of the bulls using a 95% confidence interval.

The mean height of a herd of cows is 55 inches.  The standard deviation of the heights is 10 inches.  Assume that the heights are approximately normally distributed. What proportion of the cows would be expected to be between 50 and 62 inches tall?

Suppose that an 85% 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?

Assume X is a binomial random variable.  If n = 10 and p = 0.40, find P (r = 2 successes).

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.

Measures of variation include

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.

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 mean squares for breed.

Assume that the probabilities of two genetic defects (we will call them defect A and defect B) in horses are 0.05 and 0.08, respectively.  If these two genetic defects represent independent events, what is the probability that a horse will have both of these genetic defects?

A statistician evaluated the winning strategies of teams in the National Football League (NFL).  He used actual NFL play-by-play data to approximate the probabilities associated with certain outcomes (e.g., running plays, short pass plays, and long pass plays).  The table below shows the probability distribution for the yardage gained, X, on a running play.  A negative gain represents a loss of yards on the play. Find the probability of gaining 10 or more yards on a running play. X, Yards Gained            Probability                -4                                  0.020        -2                                  0.060        -1                                  0.070          0                                 0.150          1                                 0.130          2                                 0.110          3                                 0.090          4                                 0.070          6                                 0.090          8                                 0.060         10                                0.050         15                                0.085         30                                0.010         50                                0.004         99                                0.001