Question

In a sample of 165 children selected randomly from one town, it is found that 30 of them suffer from asthma. At the 0.05 significance level, do the data provide sufficient evidence to conclude that the percentage of all children in the town who suffer from asthma is different from 11%?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.11

Ha : p 0.11

= x / n = 30 / 165 = 0.1818

P0 = 0.11

1 - P0 = 0.89

Test statistic = z

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

= 0.1818 - 0.11 / [0.11 (1-0.11 ) / 165 ]

= 2.948

P(z > 2.948) = 1 - P(z < 2.948 ) = 0.0016

2 * 0.0016 = 0.0032

P-value = 0.0032

= 0.05    

0.0032 < 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to claim