Question

An exterminator claims that no more than 10% of the homes he treats have termite problems within 1 year after treatment. In a sample of 100 homes, local officials find that 14 had termites less than 1 year after being treated. At the 0.05 level of significance, evaluate the credibility of the exterminator’s statement. (P-Value Approach)

Answer 1

Solution :

Given that,

= 0.10

1 - = 0.90

n = 100

x = 14

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 0.14

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.10

Ha: p 0.10

Test statistics

z = ( - ) / *(1-) / n

= ( 0. - 0.10) / (0.10*0.90) /100

= 1.333

P-value = P(Z > z )

= 1 - P(Z < 1.333 )

= 1 - 0.9087

= 0.0913

The p-value is p = 0.0913, and since p = 0.0913 > 0.05, it is concluded that fail to reject the null hypothesis .