A tea grower is testing two types of plant for the weight of tea they produce. A trial is set up in which each type of plant is grown at each of 8 sites. The total weight, in grams, of tea leaves harvested from each plant is measured and shown below.
Site
A
B
C
D
E
F
G
H
Type I
225.2
268.9
303.6
244.1
230.6
202.7
242.1
247.5
Type II
215.2
242.1
260.9
241.7
245.5
204.7
225.8
236.0
The grower intends to perform a \(t\) test to examine whether there is any difference in the mean yield of the two types of plant. State the hypotheses he should use and also any necessary assumption.
Carry out the test using a \(5 \%\) significance level.
The tea grower deals with many types of tea and employs tasters to rate them. The tasters do this by giving each tea a score out of 100. The tea grower wishes to compare the scores given by two of the tasters. Their scores for a random selection of 10 teas are as follows.
Tea
Q
R
S
T
U
V
W
X
Y
Z
Taster 1
69
79
85
63
81
65
85
86
89
77
Taster 2
74
75
99
66
75
64
96
94
96
86
Use a Wilcoxon test to examine, at the \(5 \%\) level of significance, whether it appears that, on the whole, the scores given to teas by these two tasters differ.