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If we roll a single die, the sample points are 1, 2, 3, 4, 5, or 6.  Consider the following two events:      Event A:  toss an even number on the die      Event B:  toss a number less than or equal to 3 on the die Calculate the probability of the intersection of events A and B:  P( A ∩ B).

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.

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 We want to test our assumption of a positive correlation between number of eggs ovulated and number of pigs in the litter.  State the appropriate null and alternative hypotheses.  Using a significance level of α = 0.05, do you reject or not reject the null hypothesis?  Explain.

A sales representative for a seedcorn company tells his boss that within the past year he has contacted 80% of the farmers in his sales district.  However, his boss makes random phone calls to 36 farmers in the sales district and finds that the sales rep only contacted 24 of them in the past year. Based on the hypothesis test, what should the boss conclude?  Explain.

In seeking a free agent NFL running back, a general manager is looking for a player with a high mean for yards gained per carry and a small standard deviation.  Suppose the GM wishes to compare the mean yards gained per carry for two free agents based on independent random samples of their yards gained per carry.  Data from last year’s pro football season indicate that σ1 and σ2 are both equal to approximately 5 yards.  If the GM wants to estimate the difference in means for yards gained per carry by the two running backs correct to within 1 yard with a confidence level of 0.90, how many carries would have to be observed for each of the two players?  Assume equal sample sizes.

We randomly select 100,000 samples of size n from a population.  We calculate the sample mean (X-bar) for each of the 100,000 random samples and graph the relative frequency distribution for these 100,000 values of X-bar.  This relative frequency distribution is called the ____________________ of X-bar.

The variable measured in an experiment (e.g., weights of dogs, litter sizes of rabbits, etc.) is called the ____________.

The weights (in pounds) of 17 pigs are used to construct the following stem-and-leaf display (the first two digits were used as the stem and the last digit was used as the leaf): Stem                   Leaf                                       16          0     5 17          — 18          — 19          — 20          — 21          — 22          2     4     6 23          0     9 24          0     1     2     3     4     5     9 25          3 26          — 27          — 28          0     5   Based on this stem-and-leaf display, the median weight is __________ lb.

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                                                                                      Derive the equation for the regression line.  What would be the predicted fleece weight of a ewe that weighs 152 lb?

A farmer weighs his calves on the day they are weaned.  The weight of the lightest calf is 300 lb and the weight of the heaviest calf is 650 lb.  Based on this information, which measure of variation could be calculated?