Use only hand calculators on this exam; Minitab or any other computer software is not allowed. The textbook (but no other notes) may be used during the exam. Be sure to submit all your work in order to receive partial credit. For example, when performing hypothesis tests it is necessary that you define the hypotheses, sketch the rejection region, and show computations for the test statistic.
1. Find the critical value x20.99, associated with a χ2 curve with 10 degrees of freedom.
2. Find the critical value having an area of 0.05 to its right for an F-curve with 8 numerator degrees of freedom and 15 denominator degrees of freedom.
3. A random sample of 100 adults was recently gathered in order to explore a possible relationship between alcohol consumption and high blood pressure. The results are provided in the contingency table below. Your job is to determine if drinking status is independent of high blood pressure.
a. Define the null and alternative hypotheses associated with the χ2 test for independence.
b. Complete the contingency table by finding expected values.
c. Let α = 0.10. Find and sketch the rejection region associated with this hypothesis test.
d. Compute the χ2 test statistic and state your conclusion.
4. The types of raw material used to construct stone stools found at the archaeological site Casa del Rito are shown below. (Bandelier Archaeological Excavation Project edited by Kohler and Root). A random sample of 1486 stone tools are obtained from a current excavation site.
Test the claim that the regional distribution of raw materials fits the distribution at the current evaluation site. State null and alternative hypothesis.
Let o: 0.10. Find and sketch the rejection region associated with this hypothesis test.
Compute the y2 test statistic and state your conclusion.
5. The presence of harmful insects in farm fields is detected by erecting boards covered with a sticky substance and then examining the insects trapped on the board. To investigate which colors are most attractive to cereal leaf beetles, researchers placed six boards of each of four colors in a field of oats. The table below gives data on the number of cereal leaf beetles trapped.
a. Compare the means for the four colors.
b. Test the hypothesis that the color of the board has no effect in attracting cereal leaf beetles at cr:0.05, assuming that the number of insects trapped follows a normal distribution and that the standard deviations are the same for all colors.
c. Do these assumptions seem reasonable? Why or why not?
6. Manatees are large sea creahrres that live in the shallow water along the coast of Florida. Many manatees are injured or killed each year by powerboats. Here are the data on manatees killed and powerboat registration (in thousands of boats) in Florida for the period 1984 to 1990.
7. Applicants for a particular job that involves extensive travel in Spanish speaking countries, must take a proficiency test in Spanish. The sample data below was obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test.
a. What is the correlation coefficient, r?
b. At the 5o/olevel of significance, do the data provide sufficient evidence to conclude that the slope of the population regression line is not zero and hence that the number of years of study is useful as a predictor of score on the test? Do the data provide sufficient evidence to conclude that the number of years of study and test score are linearly positively correlated? Use cr : 0.01.
c. Do the data provide sufficient evidence to conclude that the number of years of study and test score are linearly positively correlated? Use α = 0.01