For questions 8-18, refer to the following information: In 2004, a team of researchers published a study of contaminants in farmed salmon. Fish from many sources were analyzed for 14 organic contaminants. The study expressed concerns about the level of contaminants found. One of those was the insecticide mirex, which has been shown to be carcinogenic and is suspected to be toxic to the liver, kidneys, and endocrine system. Dioxins are also highly toxic and can cause reproductive and developmental problems, damage the immune system, interfere with hormones, and cause cancer. Using a 0.05 significance level, you need to test the claim that the dioxin level can be used to predict the mirex level. The researchers generated the following results using SAS software; however, they do not know how to interpret any of the output. Confident of your statistical abilities, they have come to you with their output and a list of questions. It's now your job to help them interpret their output. Don't let them down!

Analysis of Variance

Sum of Mean

Source DF Squares Square F Value Pr > F

Model A 0.17476 0.17476 135.64 <.0001

Error 148 0.19068 C

Corrected Total 149 B

Root MSE 0.03589 R-Square 0.4782

Dependent Mean 0.09134 Adj R-Sq 0.4747

Coeff Var 39.29746

Parameter Estimates

Parameter Standard

Variable DF Estimate Error t Value Pr > |t|

Intercept 1 0.03861 0.00539 7.16 <.0001

Dioxin 1 0.11848 0.01017 D <.0001

1. What type of analysis is this? (1 point)

1. Two-sample t-test
2. Paired t-test
3. Simple linear regression
4. Multiple linear regression
5. Contingency table analysis

1. What are the independent and dependent variables? (1 point)

1. Dependent variable is unknown, independent variable = dioxin level
2. Dependent variable is unknown, independent variable = mirex level
3. Dependent variable = mirex level, independent variable = dioxin level
4. Dependent variable = dioxin level, independent variable = mirex level
5. Variable order does not matter here, i.e. (x, y) is the same as (y, x). Either mirex or dioxin level can be the independent variable. The other is then the dependent variable.

1. What are the most appropriate null and alternative hypotheses for this analysis? (1 point)

1. H₀: = 0, H₁: 0
2. H₀: ₀ = 0, H₁: ₀ 0
3. H₀: b₀ = 0, H₁: b₀ 0
4. H₀: ₁ = 0, H₁: ₁ 0
5. H₀: b₁ = 0, H₁: b₁ 0

1. What is the size of our sample used in the model? (1 point)

1. 1
2. 148
3. 149
4. 150
5. Cannot be determined from the given information

For questions 12-14 refer to the following:In the analysis of variance table, someone replaced 3 important values with the letters A, B and C. You need to find these missing pieces.

1. Model degrees of freedom (df), labeled A (1 point)

1. 150
2. 149
3. 148
4. 2
5. 1

1. Total Sum of Squares, labeled B (1 point)

1. 0.1335
2. 0.3654
3. 0.1748
4. 0.1907
5. There is no such thing as total sum of squares (it should be left blank)

1. Mean Square Error, labeled C (1 point)

1. 0.0001
2. 0.0013
3. 0.0359
4. 0.1907
5. 0.4782

1. What is the value of the test statistic and the p-value that can be used to test the null hypothesis? (1 point)

1. t = 11.65, p < 0.0001
2. t = 7.16, p < 0.0001
3. t = 0.12, p < 0.0001
4. F = 135.64, p < 0.0001
5. Both a and d are correct
6. Both b and d are correct
7. Both c and d are correct

1. Using a 0.05 significance level, what decision and conclusion should you make regarding the null hypothesis? (1 point)

1. Because p-value > 0.05, we fail to reject H₀ and conclude that dioxin levelcannot be used to predict mirex level.
2. Because p-value > 0.05, we reject H₀ and conclude thatdioxin levelcan be used to predictmirex level.
3. Because p-value < 0.05, we reject H₀ and conclude that dioxin levelcannot be used to predict mirex level.
4. Because p-value < 0.05, we fail to reject H₀ and conclude that dioxin levelcannot be used to predict mirex level.
5. Because p-value < 0.05, we reject H₀ and conclude that dioxin level can be used to predict mirex level.

1. What is the marginal change mirex level, i.e. by how many units does mirex level change when dioxin level increases by 1 unit? (1 point)

1. Increases by 47.8%
2. Decreases by 0.12 units
3. Increases by 0.12 units
4. Decreases by 0.039 units
5. Increases by 0.039 units

1. What is the estimated value of the linear correlation coefficient and how do we best interpret this value? (1 point)

1. r = 0.4782, so 47.82% of the variation in mirex level can be explained by the linear relationship between mirex level and dioxin level.
2. r = 0.4782, so 69.15% of the variation in mirex level can be explained by the linear relationship between mirex level and dioxin level.
3. r = 0.6915, so 69.15% of the variation in mirex level can be explained by the linear relationship between mirex level and dioxin level.
4. r = 0.6915, so 47.82% of the variation in mirex level can be explained by the linear relationship between disease activity score and dioxin level.
5. r = 0.2397, so 23.97% of the variation in mirex level can be explained by the linear relationship between mirex level and dioxin level.