Question

Is the proportion of deaths from heart disease less in the Medication group than in the Placebo group? Test at the 5% significance level. Heart disease and Medication data:

Group Died of Heart disease Subjects

Medication 118 2900

Placebo 100 2100

Ho:

Ha:

Test statistic:

p-val:

Statistical Conclusion:

Conclusion in plain English:

Answer 1

Answer)

Null hypothesis Ho : p1 = p2

Alternate hypothesis Ha : p1 < p2

N1 = 2900, P1 = 118/2900

N2 = 2100, P2 = 100/2100

First we need to check the conditions of normality that is if n1p1 and n1*(1-p1) and n2*p2 and n2*(1-p2) all are greater than equal to 5 or not

N1*p1 = 118

N1*(1-p1) = 2782

N2*p2 = 100

N2*(1-p2) = 2000

All the conditions are met so we can use standard normal z table to conduct the test

Test statistics z = (P1-P2)/standard error

Standard error = √{p*(1-p)}*√{(1/n1)+(1/n2)}

P = pooled proportion = [(p1*n1)+(p2*n2)]/[n1+n2]

After substitution

Test statistics z = -1.18

From z table, P(Z<-1.18) = 0.119

So, P-Value = 0.119

As the obtained P-Value is greater than the given significance 0.05.

We fail to reject the null hypothesis Ho.

We do not have enough evidence to conclude that proportion of deaths from heart disease less in the Medication group than in the Placebo group.