The mean length of time required to complete the Columbus Marathon was 4.5 hours.  The standard deviation of the times was 0.50 hours.  Assume that the racing times were approximately normally distributed.  What is the probability that a randomly selected runner completed the race in less than 3.6 hours?

An animal scientist wants to determine the degree of association between carcass quality grade (variable X) and selling price per pound of carcass (variable Y).  The data for a random sample of 10 Angus steer carcasses are shown in the following table. Quality grade, X Carcass price per pound, Y 5 $1.09 7 1.19 4 0.99 5 1.04 8 1.21 6 1.18 4 0.94 7 1.15 8 1.23 6 1.12 The animal scientist performs a hypothesis test using a significance level of 0.05 to determine if the correlation between carcass quality grade and carcass price per pound is greater than zero. Ho:  

Health care issues are receiving a greal deal of attention in both the academic and political arenas.  A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance.  The ages (in years) of 8 uninsured senior citizens were as follows: Senior Citizen Age 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79     Calculate the standard deviation of the ages of these 8 senior citizens.

A statistician evaluated the winning strategies of teams in the National Football League (NFL).  He used actual NFL play-by-play data to approximate the probabilities associated with certain outcomes (e.g., running plays, short pass plays, and long pass plays).  The table below shows the probability distribution for the yardage gained, X, on a running play.  A negative gain represents a loss of yards on the play. Find the probability of gaining 10 or more yards on a running play. X, Yards Gained            Probability                -4                                  0.020        -2                                  0.060        -1                                  0.070          0                                 0.150          1                                 0.130          2                                 0.110          3                                 0.090          4                                 0.070          6                                 0.090          8                                 0.060         10                                0.050         15                                0.085         30                                0.010         50                                0.004         99                                0.001                                                               

We want to use a confidence interval to estimate the proportion of students in the College of Food, Agricultural, and Environmental Sciences that are female.  What sample size would be necessary if we want to estimate the true proportion of female students correct to within 0.03 with probability 0.95?  In an earlier small-scale pilot study, we obtained an estimate of the proportion of female students (p) that was equal to 0.48.

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets – Kroger, Giant Eagle, and Meier.  Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets.  In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item                          Kroger    Giant Eagle    Meier     1) Big Thirst Towel      $1.21       $1.49          $1.59 2) Post Golden Crisp    2.78         2.99            3.35 3) Tylenol Tablets         5.98         5.29            5.98           .                              .              .                   .           .                              .              .                   . 59) Colgate Shave       0.94         1.10            1.19 60) Kidney Beans        0.45          0.56            0.38                                                                                   Identify the experimental units for this experiment.

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 line x breed interaction?  Use a significance level of 0.05.

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.  Calculate the value of the test statistic needed to test the null hypothesis.

A human gene carries a certain disease from the mother to the child with a probability rate of 0.70.  That is, there is a 70% chance that the child will get the disease.  Suppose a female carrier of the gene has three children.  Assume that the infections of the three children with the disease are independent of one another.  Find the probability that all three of the children will get the disease from their mother.

A box of Mr. Phipps Tater Crisps is supposed to contain 156 grams of potato chips.  On the side of the box it says “This package is sold by weight, not by volume.  Packed as full as practicable by modern automatic equipment, it contains full net weight indicated.  If it does not appear full when opened, it is because contents have settled during shipping and handling”.  Periodically, the Nabisco Company receives complaints that their boxes of Tater Crisps are not full (i.e., that they contain less than 156 grams of potato chips).  To test this claim, the Nabisco Company randomly samples 10 boxes and finds the average amount of potato chips held by the 10 boxes is 154 grams and the standard deviation is 30 grams. State the null and alternative hypotheses the Nabisco Company wishes to test.