Practicals 7: t- distribution and t-tests
1. Download the data "people" used in the first practicals. Plot a barplot displaying height means
with 95% confidence intervals for each of the group of people defined by sex and eye color.
2. A student measured lengths of anthers of two species of Ranunculus, R. auricomus and R.
nemorosus
The values, he obtained were as following (in mm):
Auri Nemor
5 7
6 8
4 9
6 6
5
3
8
10
Does variability in anther length significantly differ between species? Does the mean anther
length differ between species?
3. Five blocks were divided into two plots of which one was fertilized and the other not. The
experiment looked like this in the field:
Resulting plant biomass was as following
Block 1 2 3 4 5
Fertilized 23 25 36 19 22
Non-
fertilized
20 24 33 18 21
Does fertilizer application affect biomass production?
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A. Temperature of water in one pot was measured by different thermometers manufactured by
two companies: Termom and Celsimet. Each of them provided 10 thermometers for the testing,
The aim of the testing was to detect potential systematic bias (whether the thermometers of one
company show in average different values from those made by the other) and whether there is a
difference in accuracy. The data were as following:
Termom: 18, 19, 18, 17, 16, 19, 18, 17, 19, 18 Celsimet: 17, 15, 21, 20, 19, 22, 15, 16 ,18, 17
Test both differences in mean values and in the accuracy between the two manufacturers.
Would you buy a thermometer produced by any of these companies?
B. 10 rats were fed by nutrition enriched in magnesium since their birth additional ten control
rats were fed by the same nutrition except for that no extra Magnesium was added. The
researchers expected that Mg should have a positive effect on the number of erythrocytes. The
results of erythrocyte counting were following:
+Mg: 85, 89, 79, 80, 91, 95, 79, 88, 89, 90.
Control: 79, 80, 75, 79, 80, 71, 75, 80, 76, 80.
Does the assumption on positive effect of Mg on erythrocytes hold?
C. Heights of siblings (brother and sister) were measured at their adult age in eight families. The
results (height in cm) are summarized in the table below.
family brother sister
1 198 165
2 164 162
3 173 158
4 180 177
5 188 178
6 169 170
7 181 165
8 174 159
Is there any significant difference in height between siblings of different sex?
D. Days with snow cover per year were monitored in Brno in 15 successive years. The resulting
numbers were as following.
year 199
8
199
9
200
0
200
1
200
2
200
3
200
4
200
5
200
6
200
7
200
8
200
9
2010 201
1
201
2
days
with
snow
cover
32 50 58 39 49 44 42 48 39 75 28 69 50 64 48
Is the mean number of days with snow cover significantly different from 58 days predicted for
Brno on the basis of a global climatic model?
E. Wine was cultivated on 8 wine-yards in the Niederösterreich region. Red grape varieties
Cabernet Sauvignon and Zweigeltrebe were cultivated on each of the wine-yards. Grapes were
harvested on the same date, pressed and glucose content in the resulting juice was measured.
The results are summarized in the table below:
Glucose (kg per hectolitre)
Vineyard Cabernet Sauvignon Zweigeltrebe
1 19.5 19.2
2 17.5 18.4
3 19.7 20.3
4 17.2 17.4
5 18 20.1
6 19.8 19.5
7 17.9 17.9
8 18.4 18.9
Do the two wine varieties significantly differ in mean glucose content?
F. Speed of swimming of two frog species was measured by a behavioral biologist. Following
data were obtained.
Frog ID Species speed (cm s-1
)
1 Bufo bufo 7.8
2 Bufo viridis 6.5
3 Bufo viridis 6.9
4 Bufo bufo 7.1
5 Bufo bufo 6.7
6 Bufo viridis 7.1
7 Bufo viridis 7.0
8 Bufo viridis 6.5
9 Bufo bufo 7.0
10 Bufo viridis 6.4
11 Bufo bufo 6.9
12 Bufo viridis 7.2
13 Bufo bufo 7.5
14 Bufo bufo 7.2
Do the two species significantly differ in speed of swimming?
G. A farmer tested yield difference between two varieties of rye. He cultivated each of them on
six fields andweere obrained measured the grain yield (in tonnes per hectare). Following
numbers were obtained
Field Variety yield (tonnes per hectare)
1 Champion 5.5
2 Miracle 6.1
3 Champion 5.7
4 Champion 6.0
5 Miracle 5.3
6 Miracle 5.8
7 Champion 6.4
8 Miracle 6.0
9 Miracle 5.5
10 Champion 6.4
11 Miracle 5.5
12 Champion 6.1