In a pizza takeout restaurant, the following probability distribution was obtained.  The random variable X represents the number of toppings for a large pizza.                                                                                      x             0          1          2          3          4          P(x)          0.30     0.40     0.20     0.06     0.04          Calculate the variance of this discrete probability distribution.

A two-factor factorial experiment is conducted to compare litter sizes of Yorkshire and Landrace sows derived either from a line unselected for litter size or from a line that has gone through 15 years of selection for increased litter size.  Two sows of each breed are randomly selected from each line.  Their litter sizes are as follows:                                   Yorkshire       Landrace            Unselected line               8                     9                                        9                    10 Selected line                 11                    11                                      10                      9                                                                                     The partially completed ANOVA table is as follows:  Source             df             SS                MS            F  Total                              7.875 Line                               3.125            3.125       3.57 Breed Line x Breed Error                              3.500            0.875                                                                                       What is the correct conclusion regarding the hypothesis test for breed?  Use a significance level of 0.05.

A plant scientist wants to determine the average yield (in bushels per acre) of brand X corn in Ohio.  Five thousand Ohio corn fields are planted using brand X.  The plant scientist is able to obtain data for the yields of 500 of these 5,000 fields.  The average yield of these 500 fields planted to brand X is 175 bushels per acre.  What does the value of 175 bushels per acre represent?

A swine producer wants to know if the average weight of his pigs is different from the breed average of 230 lb.  He selects a random sample of 16 weights from pigs in his herd and calculates a sample mean of 220 lb and a sample standard deviation of 25 lb.  Assume that he wants to detect departure from 230 lb in either direction and that he uses a significance level of 0.10.  The correct conclusion is:

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

The probability of a male offspring is 1/2 and the probability of a female offspring is 1/2.  What is the probability that a mare will give birth to a female offspring in four consecutive years, assuming that the sexes of the offspring in different years are independent events?

The grades of 8 students on an exam were as follows: Student Grade 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79     Find the range for the grades of these 8 students.

Suppose that we want to make an inference about the population proportion (p).  For sufficiently large sample sizes, the sampling distribution of p-hat is approximately normally distributed with mean equal to __________.

Two fair coins are tossed and the events A and B are defined as follows: A: {At least one head appears} B: {Exactly one head appears} Find P (B)

In a controlled laboratory environment, independent random samples of 10 adults and 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable.  The study provided the following results:                                               Adults         Children Sample size                            10                 10 Sample mean (in degrees)   77.5              74.5 Sample variance                       4.5                2.5 Which one of the following is the correct 99% confidence interval for the true difference in population mean temperatures that adults and children find most comfortable?