The Central Limit Theorem says that the sampling distribution of the sample mean is approximately normal under certain conditions.  Which of the following is a necessary condition for the Central Limit Theorem to be used?

It seems reasonable to assume that the number of times a team punts the ball in a football game would be negatively correlated with the number of points that the team scores (i.e., if a team is forced to punt frequently they are probably not moving the ball very well and probably are not scoring many points).  Number of punts (variable X) and number of points scored (variable Y) for a particular team in a random sample of five games are as follows: Number of Punts, X          Number of Points, Y              2                                         35              5                                         14              3                                         21              2                                         21              2                                         28   Calculate the Y-intercept of the least squares line for the regression of Y (points scored) on X (number of punts).

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.

The mean weaning weight in a herd of beef cattle is 520 lb and the standard deviation of the weaning weights is 50 lb.  The probability of a calf weighing less than X lb is 0.20.  What is the value of X?

Two disadvantages of using the “pulling numbers of a hat” method of obtaining a random sample are (1) that it is not feasible for large populations (e.g., 5 million cows) and (2) it is difficult to get a thorough mixing of the pieces of paper.

The least squares line is the best-fitting straight line to the data in that the least squares line is the one that minimizes the sums of squares of deviations of points from the line.

Assuming that n1 = n2, find the sample sizes needed to estimate (p1 – p2) correct to within 0.07 with probability 0.90.  Assume that there is no prior information available to obtain sample estimates of p1 and p2.

A population of rabbits has a mean weight of 12 lb with a standard deviation of 3 lb.  A rabbit breeder selects 1,000 samples of 36 rabbits each from this population, calculates the mean weight of the rabbits in each of these 1,000 samples, and then graphs the 1,000 sample means.  The standard deviation of the 1,000 sample means is expected to be equal to:

The fleece weights of 8 sheep (in pounds) are as follows: 5     6     7     8     9     10     10     12 For this sample of 8 fleece weights, the range is

Find the mean of a binomial probability distribution with a sample size of n = 25 and a probability of success of 0.30.