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We have an event A and an event B, where    P (A) = 0.80     P (B) = 0.20     P (A intersect B) = 0.10 Find P (A union B).

An animal scientist conducts a study to estimate the proportion of cows of the Charolais breed that require assistance during calving.  A random sample of 500 Charolais cows is selected.  Results of the study show that 100 of the 500 cows in the sample required assistance in giving birth.  What is the point estimate of the true population proportion (p) of Charolais cows that require assistance during calving?

A Randomized Block Design is used to compare fleece weights of three breeds of sheep – Merino, Suffolk, and Dorset (we can think of the three breeds as being the three treatments).  The sheep are divided into two weight classes (i.e., two blocks).  Block one contains sheep weighing less than 150 lb and block two contains sheep weighing more than 150 lb.  The fleece weights (in pounds) are as follows:                    Merino          Suffolk          Dorset Block 1          13                  8                  9 Block 2          14                  9                 11                                                                          The partially completed ANOVA table for this experiment is as follows: Source     df          SS            MS            F      Total                29.33333 Breed              26.33333     13.16667    79.00003 Block                     Error                 0.33333        0.16667              We want to test the null hypothesis that the three breed means are equal vs. the alternative hypothesis that at least two of the breed means are different.  Using a signficance level of 0.05, which one of the following statements is the correct conclusion?

Which of the following is not one of the properties of the sampling distribution of the sample mean?

The normal approximation to a binomial probability distrubtion is reasonably good even for small sample sizes (say, n as small as 10) when p = 1.0 and the distribution of X is therefore symmetric about its mean.

Assume that 20% of all pigs die between birth and weaning.  In a random sample of 300 births, let X be the number of pigs that die between birth and weaning.  Using the normal approximation to the binomial, find the approximate probability that the number of pigs in the sample of 300 that die between birth and weaning is less than or equal to 50.

A study was conducted to determine whether a student’s final grade in a high school math class is linearly related to his or her performance on the math ability test administered before college entrance.  The math test scores and final grades for a random sample of 10 students are shown below. Final Grade in Math Class (X)          Math Ability Test Score (Y) 65                                                             39 78                                                             43 52                                                             21 82                                                             64 92                                                             57 89                                                             47 73                                                             28 98                                                             75 56                                                             34 75                                                             52 Given that the variance of the final grades in the math class (i.e., variable X) is 228.4444 and the variance of the math ability test scores (i.e, variable Y) is 274.8889, calculate the slope of the regression line for the regression of Y on X.

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                                                                                       State the null and alternative hypothesis for the location x breed interaction.

________________ can be applied to any data set, regardless of the shape of the distribution.

It seems reasonable to assume that ovulation rate and litter size in pigs would be positively correlated.  In other words, if a sow releases more eggs (i.e., ova) in a given estrus period, she will probably end up producing more pigs in her litter.  Number of eggs ovulated and litter size for a random sample of 6 sows are as follows: Number of Eggs, X       Number of Pigs Born, Y                14                                  7                15                                  7                16                                  9                17                                 10                17                                 10                17                                  11 Given that the variance of Y (number of pigs born) is 2.8 pigs2 (in the interest of time, I have calculated this value for you), find the correlation between X and Y.