Practicals 7: t- distribution and t-tests
1. Import again 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. Import again the “lettuce” data, which were used in the graph plotting workshops. Test
whether green- and red-leaved lettuce varieties differ in harvest mass and harvest date. Check
the patterns on corresponding plots.
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. 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 results
of erythrocyte counting in blood of each of the rats 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 Mg affect number of erythrocytes?
B. 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?
C. Days with snow cover per year were monitored in Brno in 15 successive years. The resulting
numbers were as following.
year 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
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?
D. 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?
E. 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?
F. 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