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A scientist conducts an experiment to determine if the mean alkalinity level of water specimens from the Olentangy River is greater than 50 milligrams per liter (mpl).  She selects a random sample of 100 water specimens from the river and finds a sample mean of 67.8 mpl and a sample standard deviation of 14.4 mpl.  She decides to test the hypothesis using a significance level of 0.01.  Using this information concerning the alkalinity level of water from the Olentangy River, which one of the following statements is correct?

Assume that we want to test the null hypothesis that the correlation between two variables is 0 vs. the alternative hypothesis that the correlation between these two variables is not equal to 0.  Based on a random sample of n = 15 observations, we calculate the sample correlation coefficient of r = 0.20.  Using a significance level of 0.05, which one of the following statements represents the correct conclusion?

The person in charge of genetic evaluation of beef cattle wants to know if birth weights of calves are influenced by breed and if they are influenced by the region of the U.S. (i.e., Northern U.S. vs Southern U.S.) in which the calf is born.  She has heard that calves born in the South are usually lighter at birth than are calves born in the North.  In order to answer these questions, she sets up a 2 x 3 factorial experiment with 3 replications and obtains the birth weights (in pounds) shown in the following table:                   Angus       Charolais       Simmental North             85                93                 91                       85                92                 92                       83                94                 92   South            85                84                  82                      76                85                   83                      74                83                   83       The partially completed ANOVA table is as follows: Source               df             SS            MS          F       Total                                 548.00 Location Breed                               174.33       87.165     13.643 Location x breed                  9.00         4.500 Error                                                                                         State the null and alternative hypothesis for location.  Using a significance level of α = 0.05, do you reject or not reject the Ho?

A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in Columbus.  Suppose an experiment consists of randomly selecting one of the returned questionnaires.  Consider the events:    Event A:  the home is constructed of brick    Event B:  the home is more than 30 years old    Event C:  the home is heated with oil A home that is constructed of brick and is less than or equal to 30 years old would be represented by which one of the following?

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 mean of these 1,000 sample means is expected to be equal to:

A perfect negative correlation between variables X and Y indicates that the correlation between these two variables is equal to __________.

Find the area under the normal curve between z = -1.25 and z = 1.75.

If an interaction exists in a factorial experiment, tests of the main effects are not relevant, because differences in the mean levels of factor A are not the same across all levels of factor B.

The mean length of time required to complete a 5K race was 20 minutes.  The standard deviation of the times was 4 minutes.  The racing times were approximately normally distributed.  What is the probability that a randomly selected runner completed the race in less than 16 minutes?

A Randomized Block Design is used to compare fleece weights of three breeds of sheep – Merino, Suffolk, and Dorset (we can think of the three breeds as being the three treatments).  The sheep are divided into two weight classes (i.e., two blocks).  Block one contains sheep weighing less than 150 lb and block two contains sheep weighing more than 150 lb.  The fleece weights (in pounds) are as follows:                    Merino          Suffolk          Dorset Block 1          13                  8                  9 Block 2          14                  9                 11                                                                          The partially completed ANOVA table for this experiment is as follows: Source     df          SS            MS            F      Total                29.33333 Breed              26.33333     13.16667    79.00003 Block                     Error                 0.33333        0.16667              The correct degrees of freedom for total, breed, block, and error, respectively are: