Pearson Edexcel Level 3 GCE Further Mathematics Advanced Subsidiary Further Mathematics options 23: Further Statistics 1 (Part of options B, E, F and G) 8FM0/231. Stuart is investigating a treatment for a disease that a
...
Pearson Edexcel Level 3 GCE Further Mathematics Advanced Subsidiary Further Mathematics options 23: Further Statistics 1 (Part of options B, E, F and G) 8FM0/231. Stuart is investigating a treatment for a disease that affects fruit trees. He has 400 fruit
trees and applies the treatment to a random sample of these trees. The remainder of the
trees have no treatment. He records the number of years, y, that each fruit tree remains
free from this disease.
The results are summarised in the table below.
Treatment
Applied Not applied
Number of years free
from this disease
y < 1 15 25
1 y < 2 35 61
2 y 124 140
The data are to be used to determine whether or not there is an association between the
application of the treatment and the number of years that a fruit tree remains free from
this disease.
(a) Calculate the expected frequencies for
(i) Applied and y < 1
(ii) Not applied and 1 y < 2
(2)
The value of
O E
−E
( )
∑
2
for the other four classes is 2.642 to 3 decimal places.
(b) Test, at the 5% level of significance, whether or not there is an association between
the application of the treatment and the number of years a fruit tree remains free
from this disease.
You should state your hypotheses, test statistic, critical value and conclusion clearly.
(5)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________
[Show More]