Page 28 (2.1.2, 2.1.3)
  1. identify the variable(s) in the study,
  2. for each variable tell the type of variable (e.g., categorical and ordinal, discrete, etc.),
  3. identify the observational unit (the thing sampled), and
  4. determine the sample size.

2.1.2

A. A physician measured the height and weight of each of 37 children.

  1. Variables: height, weight
  2. Variable types:
    • height: quantitative/numeric—continuous
    • weight: quantitative/numeric—continuous
  3. Observational unit: A child
  4. Sample size: 37

B. During a blood drive, a blood bank offered to check the cholesterol of anyone who donated blood. A total of 129 persons donated blood. For each of them, the blood type and cholesterol levels were recorded.

  1. Variables: blood type, cholesterol levels
  2. Variable types:
    • blood type: Categorical
    • cholesterol levels: quantitative/numeric—continuous
  3. Observational unit: Blood donation from one person
  4. Sample size: 129

2.1.3

A. A biologist measured the number of leaves on each of 25 plants.

  1. Variables: count of leaves
  2. Variable types:
    • Count of leaves: quantitative/numeric—discrete
  3. Observational unit: A plant
  4. Sample size: 25

B. A physician recorded the number of seizures that each of 20 patients with severe epilepsy had during an eight-week period.

  1. Variables: Count of seizures
  2. Variable types:
    • Count of seizures: quantitative/numeric—discrete
  3. Observational unit: A patient
  4. Sample size: 20
Page 39 (2.2.4, 2.2.5) – Construct a dotplot of the data.

2.2.4 A dendritic tree is a branched structure that emanates from the body of a nerve cell. As part of a study of brain development, 36 nerve cells were taken from the brains of newborn guinea pigs. The investigators counted the number of dendritic branch segments emanating from each nerve cell. The numbers were as follows:

23 30 54 28 31 29 34 35 30 27 21 43 51 35 51 49 35 24 26 29 21 29 37 27 28 33 33 23 37 27 40 48 41 20 30 57

2.2.5 Consider the data presented in Exercise 2.2.4. Construct a frequency distribution and display it as a table and as a histogram.

Frequency distribution:

##    num_branch_segments Freq
## 1                   20    1
## 2                   21    2
## 3                   23    2
## 4                   24    1
## 5                   26    1
## 6                   27    3
## 7                   28    2
## 8                   29    3
## 9                   30    3
## 10                  31    1
## 11                  33    2
## 12                  34    1
## 13                  35    3
## 14                  37    2
## 15                  40    1
## 16                  41    1
## 17                  43    1
## 18                  48    1
## 19                  49    1
## 20                  51    2
## 21                  54    1
## 22                  57    1

Page 44 (2.3.10)

2.3.10 As part of a classic experiment on mutations, 10 aliquots of identical size were taken from the same culture of the bacterium E. coli. For each aliquot, the number of bacteria resistant to a certain virus was determined. The results were as follows:
14 15 13 21 15 14 26 16 20 13

  1. Construct a frequency distribution of these data and display it as a histogram.
  2. Determine the mean and the median of the data and mark their locations on the histogram.

## [1] "Median :15.0  " "Mean   :16.7  "
Page 51 (2.4.3)

2.4.3 In a study of milk production in sheep (for use in making cheese), a researcher measured the 3-month milk yield for each of 11 ewes. The yields (liters) were as follows:
56.5 89.8 110.1 65.6 63.7 82.6 75.1 91.5 102.9 44.4 108.1

  1. Determine the median and the quartiles.
  2. Determine the interquartile range.
  3. Construct a boxplot of the data.
## 1st_quartile       median 3rd_quartile 
##        64.65        82.60        97.20

Page 58 (2.5.3ab, 2.5.4)

2.5.3 The rowan (Sorbus aucuparia) is a tree that grows in a wide range of altitudes. To study how the tree adapts to its varying habitats, researchers collected twigs with attached buds from 12 trees growing at various altitudes in North Angus, Scotland. The buds were brought back to the laboratory and measurements were made of the dark respiration rate. The accompanying table shows the altitude of origin (in meters) of each batch of buds and the dark respiration rate (expressed as ml of oxygen per hour per mg dry weight of tissue).

##    tree altitude respiration_rate
## 1     1       90             0.11
## 2     2      230             0.20
## 3     3      240             0.13
## 4     4      260             0.15
## 5     5      330             0.18
## 6     6      400             0.16
## 7     7      410             0.23
## 8     8      550             0.18
## 9     9      590             0.23
## 10   10      610             0.26
## 11   11      700             0.32
## 12   12      790             0.37
  1. Create a scatterplot of the data.

  1. If your software allows, add a regression line to summarize the trend.
## `geom_smooth()` using formula 'y ~ x'

  1. If your software allows, create a scatterplot with a lowess smooth to summarize the trend.
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

2.5.4 A group of college students were asked how many hours per week they exercise. The answers given by 12 men were as follows:
6 0 2 1 2 4.5 8 3 17 4.5 4 5

The answers given by 13 women were as follows:
5 13 3 2 6 14 3 1 1.5 1.5 3 8 4

  1. Construct parallel boxplots of the male and female distributions.
  2. Describe the two boxplots, including how they compare to each other.

-b The two boxplots for female and male exercise hours depict data that is clustered generally in the same region–with the first quartile around 2 hours and the third quartile around 6 hours for both genders. The median is slightly higher for males (~4 hours) than it is for females (~3 hours), and the whiskers for the male data also extend further than for the females.

Page 66 (2.6.5, 2.6.6, 2.6.8, 2.6.15)

2.6.5 A plant physiologist grew birch seedlings in the greenhouse and measured the ATP content of their roots. (See Example 1.1.3.) The results (nmol ATP/mg tissue) were as follows for four seedlings that had been handled identically.

1.45 1.19 1.05 1.07
Calculate the mean and the SD.

## [1] "mean: 1.190"
## [1] "standard deviation: 0.184"

2.6.6 Ten patients with high blood pressure participated in a study to evaluate the effectiveness of the drug Timolol in reducing their blood pressure. The accompanying table shows systolic blood pressure measurements taken before and after 2 weeks of treatment with Timolol.
Calculate the mean and SD of the change in blood pressure (note that some values are negative). Blood pressure (mm HG) Patient Before After Change 1 172 159 -13 2 186 157 -29 3 170 163 -7 4 205 207 2 5 174 164 -10 6 184 141 -43 7 178 182 4 8 156 171 15 9 190 177 -13 10 168 138 -30

## [1] "mean change in blood pressure: -12.400"
## [1] "standard deviation change in blood pressure: 17.589"

2.6.8 In a study of the lizard Sceloporus occidentalis, biologists measured the distance (m) run in 2 minutes for each of 15 animals. The results (listed in increasing order) were as follows:

18.4 22.2 24.5 26.4 27.5 28.7 30.6 32.9 32.9 34.0 34.8 37.5 42.1 45.5 45.5

  1. Determine the quartiles and the interquartile range.
  2. Determine the range.
##    distances    
##  Min.   :18.40  
##  1st Qu.:26.95  
##  Median :32.90  
##  Mean   :32.23  
##  3rd Qu.:36.15  
##  Max.   :45.50
## [1] "IQR: 9.200"