If we roll a single die, the sample points are 1, 2, 3, 4, 5, or 6.  Consider the following two events:      Event A:  toss an even number on the die      Event B:  toss a number less than or equal to 3 on the die List the sample points that would be included in the union of events A and B (i.e., A U B).

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   What are the correct null and alternative hypotheses if we want to test that these two variables are positively correlated?

The Environmental Science & Technology journal reported on a study of contaminated soil in The Netherlands.  A total of 81 soil specimens were sampled, dried, and analyzed for the contaminant cyanide.  The cyanide concentation (in milligrams per kilogram, mg/kg, of soil) of each soil specimen was determined using an infrared microscopic method.  The samples had a mean cyanide level of 95 mg/kg and a standard deviation of 50 mg/kg.  The authors of the journal article tested the hyothesis that the true mean cyanide level in the soil in The Netherlands was less than 100 mg/kg using a significance level of α = 0.10. Calculate the value of the test statistic needed to test this hypothesis.

A swine producer reads a report stating that the average litter size in the US is 7.8 pigs per litter.  However, he feels that the average litter size on his farm is not 7.8 pigs/litter (he wants to detect departure in either direction from the hypothesized mean of 7.8 pigs/litter).  To test his hypothesis, he reviews his records for the past year and randomly selects 16 litters, which averaged 8.0 pigs/litter.  The standard deviation is 1 pig/litter. State the null and alternative hypothesis.

If we roll a single die, the sample points are 1, 2, 3, 4, 5, or 6.  Consider the following two events:      Event A:  toss an even number on the die      Event B:  toss a number less than or equal to 3 on the die Calculate the probability of the union of events A and B:  P( A U B).

Find the standard deviation of a binomial probability distribution with a sample size of n = 40 and a probability of success of 0.40.

Which one of the following statements about the sampling distribution of the sample mean is incorrect?

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 or is not heated with oil would be represented by which one of the following?

The average litter size in Ohio is approximately 8 pigs per litter.  Owners of a particular breed would like to prove that the mean litter size of their breed is greater than 8 pigs per litter.  Therefore, they want to test:      Ho:  μ = 8 pigs/litter      Ha:  μ > 8 pigs/litter They obtain a random sample of 100 litter size records from sows of this breed and find a sample mean of 8.4 pigs per litter and a sample standard deviation of 1 pig per litter.  They decide to use a significance level of α = 0.01. What is the appropriate test statistic needed to test the null hypothesis?

Independent random samples of litter sizes were selected from the Yorkshire and Landrace breeds of swine, with the following results: Yorkshire Landrace 8 7 9 8 10 9 8 8 9 7 10   We want to analyze these data using Analysis of Variance with a Completely Randomized Design. Calculate the Total Sums of Squares.