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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.

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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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