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 variance of variable X (number of punts in a football game).

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 Use the deterministic component of the straight-line probabilistic model to obtain the predicted litter size if a sow ovulates 17 eggs.

An animal scientist is interested in determining the proportion of ewes that give birth to twins.  Rather than examine the records for all ewes in the United States, he randomly selects 500 ewes and finds that 220 of them gave birth to twins.  The animal scientist knows that the sample size of n = 500 is large enough for large-sample confidence interval procedures to be valid, because:

A randomized block design was used to compare the mean responses for three treatments.  Four blocks of three homogeneous experimental units were selected, and each treatment was randomly assigned to one experimental unit within each block.  The partially completed ANOVA table for this experiment is as follows: Source               df        SS             MS          F   Total                  11       84.489 Treatments         2       12.032       6.016 Blocks                3       71.749      23.916 Error                  6         0.708        0.118             Do the data provide sufficient evidence to indicate that blocking was effective in reducing variation in the responses?  Use α = 0.05.

Scientists want to estimate the difference in twinning rate of two lines of beef cattle that have been selected for increased frequency of twin births.  Last spring, 40 of the 100 cows in Line 1 gave birth to twins.  In Line 2, 30 of the 100 cows gave birth to twins.  Find the point estimate of the true difference in population proportions of cows giving birth to twins in Lines 1 and 2.

Assuming that the two sample sizes are the same, find the sample sizes needed to estimate the difference in population proportions correct to within 0.03 with a 90% level of confidence.  From prior experience we have an estimate of p1 that it is equal to 0.70 and an estimate of p2 that is equal to 0.60.

The object upon which the response variable is measured (animals, people, etc.) is called the __________.

A ________ ________ error occurs if we fail to reject a null hypothesis when it is false.

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.

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   What would be the predicted number of points scored if the team punted 4 times in a game?