Question

In a sample of 160 children selected randomly from one town, it is found that 40 of them suffer from asthma. At the 0.05 significance level, test the claim that the proportion of all children in the town who suffer from asthma is 11%.

Answer 1

Solution :

Given that ,

n = 160

x = 40

The null and alternative hypothesis is

H0 : p = 0.11

Ha : p 0.11

This is the two tailed test .

= x / n = 40 / 160 = 0.25

P0 = 11%. = 0.11

1 - P0 = 1 - 0.11 = 0.89

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.25 - 0.11 / [0.11( 1 - 0.11 / 160 ]

= 5.66

The test statistic = 5.66

P-value = 0.0000

= 0.05   

0.0000 < 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to the test claim .