Biostats SDS 328M Homework 8 Write your answers onto one or more separate sheets of paper. Clearly mark each sheet with your

name and your lab time. Show all work for full credit.

Round all answers to at least 3 decimal places and assume, unless otherwise noted, that α=0.05

1. The Beck depression inventory and the Hamilton rating scale are two rating systems that are

commonly used to evaluate the level of depression in patients. Below are data from ten patients

who were evaluated using both scales:

Patient

1

2

3

4

5

6

7

8

9

10 Beck depression

inventory

20

11

13

22

37

27

14

20

37

20 Hamilton rating

scale

22

14

10

17

31

22

12

19

29

15 a. Sketch a scatter plot to show the relationship between these two rating scales. Use the

Beck score as the explanatory variable and the Hamilton score as the response. Based on

your graph, are the relevant assumptions of a correlation analysis met? (3pt)

b. Based on the above data, the Pearson correlation coefficient between these two scales is = 0.94 . Conduct a hypothesis test to determine if the Beck score is significantly

correlated with the Hamilton score. Include all steps for full credit. (4pt)

c. Suppose a 11th patient was entered into the study, and his scores were as follows: Beck

score =13, Hamilton score = 29. If you recalculated the correlation coefficient including

this data point, would increase, decrease, or stay the same? (1pt) Copyright © 2016 Dept. of Statistics and Data Sciences, UT Austin 2. The males of some cichlid fish species are infertile and non-territorial until they become the

socially dominant male in the presence of females. They can shift from one state to the other in

a matter of days, and the shift may be determined by the gene GnRH. As part of a study on this

gene, researchers measured the mRNA expression levels of GnRH (copies per cell) for a sample

of territorial (T) males and a sample of non-territorial (NT) males:

Cichlid Male Territorial Status 1

2

3

4

5

6

7

8

9

10

11 NT

NT

NT

NT

NT

NT

T

T

T

T

T GnRH mRNA expression level

(copies per cell)

0.61

0.37

0.70

0.98

1.34

1.03

1.79

2.02

1.29

3.13

2.84 Conduct the appropriate test to see if mRNA expression in this gene differs between territorial

and non-territorial males. Include all steps for full credit. (4pt)

3. In a study of crop losses due to air pollution, 20 separate plots of snap beans were grown in

open-top field chambers and were fumigated with various concentrations of sulfur dioxide.

After one month, the plants were harvested and the total yield of bean pods was recorded for

each chamber. Wanting to see if sulfur dioxide concentration could predict crop yield, the

researchers confirmed all assumptions of a linear regression analyses were met and calculated

the following descriptive statistics: Mean

St. Dev. SO2 Conc. (ppm)

Crop yield (kg)

0.46

1.12

0.28

0.45 = −0.68 a. Find the linear regression equation that predicts crop yield based on SO2 concentration.

(2pt)

b. Interpret the values of the slope and intercept, in the context of the problem. (2pt)

c. What is the residual of a snap bean plot that was fumigated with 0.5 ppm SO2 and

yielded 0.84 kg? (1pt)

d. Calculate a 95% confidence interval for the slope. Does this suggest that these two

variables are significantly linearly related? Why/why not? Given: SEb1 = 0.49 (3pt) Copyright © 2016 Dept. of Statistics and Data Sciences, UT Austin

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