Question

Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 2000. To look at changes in incidence over time, 5000 men in this age group were followed for 1 year starting in 2010. Fifteen new cases of MI were found.

Now suppose that 25% of patients with MI in 2000 died within 24 hours. This proportion is called the 24-hour case-fatality rate.

7.14 Of the 15 new MI cases in the preceding study, 5 died within 24 hours. Test whether the 24-hour case- fatality rate changed from 2000 to 2010.

Answer 1

Here we have to test the hypothesis that,

H : p = 5/1000 = 0.005 Vs H1 : p 0.005

where p is population proportion.

Sample proportion (p^) = 15/5000 = 0.003

npq = 5000 * 0.005 * (1 - 0.005) = 24.88 > 5

Therefore we will use here normal approximation.

From this we can conclude that the incidence rate of MI among 45-54 years old males in 2010 is significantly lower than that in 2000.

The test statistic is,

Z = -2.01

Now we have to find P-value for taking decision.

We can find P-value in excel.

syntax :

=2*NORMSDIST(z)

where z is test statistic.

P-value= 0.045

P-value < alpha (005)

Reject H0 at 5% level of significance.