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?

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).

Qualitative data are discrete.

A two-factor factorial experiment is conducted to compare fleece weights of Merino, Suffolk, and Dorset ewes fed one of two diets.  Two ewes of each breed are randomly assigned to each diet.  The fleece weights (in pounds) are as follows:                Merino            Suffolk            Dorset        Diet 1          14                   9                    8                     15                 10                    8 Diet 2           13                   8                  11                     12                    9                 12                                                                                   The partially completed ANOVA table is as follows: Source             df           SS             MS           F      Total                          66.2500 Diet                             0.0833       0.0833       0.19992 Breed                        46.5000     23.2500     55.79955 Diet x Breed              17.1667     Error                            2.5000      0.41667                                                                                       Should we test the hypotheses involving differences in mean levels of the main effects of diet and breed?  Assume that we use a significance level of 0.05.

Suppose that a random sample of 100 measurements is selected from a population with a mean = 200 lb and a variance = 1,600 lb2.  What is the mean of the sampling distribution of the sample mean?

An animal scientist is interested in determining the proportion of ewes (i.e., female sheep) that give birth to twins.  Rather than examine the records for all ewes in the United States, the animal scientist randomly selects 500 ewes and finds that 220 of them gave birth to twins. Construct a 99% confidence interval to estimate the true population proportion of ewes, p, who give birth to twins.

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 correlation coefficent for the correlation between variables X and Y.

Assume that P(A) = 0.6, P(B) = 0.3, and P(A|B) = 0.6, where A and B are two different events.  Which one of the following statements is correct?