Question

The pesticide diazinon is commonly used to treat infestations of the german cockroach, blattella germanica. A study investigated the persistence (as measured by percent of pests killed) of this pesticide on various types of surfaces. Researchers applied a 0.5% emulsion of diazinon to glass and plasterboard surfaces. After 14 days, they placed 36 randomly chosen cockroaches on each surface and recorded the number that died within 48 hours. On glass, 14 cockroaches died, while on plaster board, 26 died.

Describe a type 1 error and the related consequences in context of this problem. what is the probability of committing a type 1 error?

Answer 1

Type 1 error: Probability of reject the null hypothesis when null hypothesis is true

Let the proportion of cockroaches died on glass be p1 and that on plaster be p2

In the current question, consequence would be concluding more number of cockroaches die on plaster but actually similar number of cochroaches die on both glass and plaster.

H0: p1=p2, Ha:p1<p2

p1=14/36, n1=36, p2=26/36,n2=36

P(t*<-3.0211,58dof)=0.0019

Hence, P(Type 1 error)=0.0019