Chi-square Test, ANOVA & Regression Analysis

Unit 4 Test
1. Find the critical value Chi-square (0.99) associated with a Chi-square 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.
Drinking status Absent Present Total
non drinker 26 11 37
light to moderate 16 29 45
heavy drinker 13 5 18
Total 55 45 100

a. Define the null and alternative hypotheses associated with the Chi-square 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 Chi-square 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 is obtained from a current excavation site.
Raw Material Regional Percent of Stone Tools Observed Number of Tools at Current Excavation Site
Basalt 61.30% 906
Obsidian 10.60% 162
Welded tuff 11.40% 168
Pedernal chert 13.10% 197
Other 3.60% 53
Total 100% N = 1486

a. Test the claim that the regional distribution of raw materials fits the distribution at the current evaluation site. State the null and alternative hypothesis.
b. Let α = 0.10. Find and sketch the rejection region associated with this hypothesis test.
c. Compute the χ 2 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 colours are most attractive to cereal leaf beetles, researchers placed six boards of each of four colours in a field of oats. The table below gives data on the number of cereal leaf beetles trapped.

Colour Insects Trapped

Yellow 45 59 48 46 38 47
White 21 12 14 17 13 17
Green 37 32 15 25 39 41
Blue 16 11 20 21 14 7

a. Compare the means for the four colours.
b. Test the hypothesis that the colour of the board has no effect in attracting cereal leaf beetles at α = 0.05, assuming that the number of insects trapped follows a normal distribution and that the standard deviations are the same for all colours.
c. Do these assumptions seem reasonable? Why or why not?

6. Manatees are large sea creatures 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.
a. Complete the table.
b. Using the table, find the following values: , Sxx, Syy and Sxy.
c. Using and find the regression equation .
d. What is the coefficient of determination, r2?
e. If Florida were to limit powerboat registration to a maximum of 700,000 boats (x = 700) how many manatees could we expect to be killed?

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.

Number of Years (x): 3 4 4 2 5 3 4 5 3 2
Score (y): 57 78 72 58 89 63 73 84 75 48

Partial Minitab output is provided below.

Mintab -- Regression Analysis

The regression equation is score = 31.5 + 10.9*years

S = 5.651 R-Sq = 83.0% R-Sq(adj) = 80.9%

Analysis of Variance

Source DF SS MS F P

Regression 1 1248.6 1248.6 39.09 0.000

Residual Error 8 255.5 31.9

Total 9 1504.1

a. What is the correlation coefficient, r?
b. At the 5% level 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?
c. Do the data provide sufficient evidence to conclude that the number of years of study and test score is linearly positively correlated? Use α = 0.01.

See attached file.

Please provide detail solutions to problems.