A medical researcher is looking into the delay, in years, between first and second myocardial infarctions (heart attacks). The following table shows the results for a random sample of 225 patients.
Delay (years)
\(0 -\)
\(1 -\)
\(2 -\)
\(3 -\)
\(4 - 10\)
Number of patients
160
40
13
9
3
The mean of this sample is used to construct a model which gives the following expected frequencies.
Delay (years)
\(0 -\)
\(1 -\)
\(2 -\)
\(3 -\)
\(4 - 10\)
Number of patients
142.23
52.32
19.25
7.08
4.12
Carry out a test, using a \(2.5 \%\) level of significance, of the goodness of fit of the model to the data.
A further piece of research compares the incidence of myocardial infarction in men aged 55 to 70 with that in women aged 55 to 70 . Incidence is measured by the number of infarctions per 10000 of the population. For a random sample of 8 health authorities across the UK, the following results for the year 2010 were obtained.
Health authority
A
B
C
D
E
F
G
H
Incidence in men
47
56
15
51
45
54
50
32
Incidence in women
36
30
30
47
54
55
27
27
A Wilcoxon paired sample test, using the hypotheses \(\mathrm { H } _ { 0 } : m = 0\) and \(\mathrm { H } _ { 1 } : m \neq 0\) where \(m\) is the population median difference, is to be carried out to investigate whether there is any difference between men and women on the whole.
Explain why a paired test is being used in this context.
Carry out the test using a \(10 \%\) level of significance.