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Cockroaches The pesticide diazinon is commonly used to treat infestations of the German cockroach, Blattella germanica. A study investigated the persistence of this pesticide on various types of surfaces. Researchers applied a $0.5\%$emulsion of diazinon to glass and plasterboard. After $14$days, they randomly assigned $72$cockroaches to two groups of $36$, placed one group on each surface, and recorded the number that died within $48$hours. On glass, $18$cockroaches died, while on plasterboard, $25$died. If$p_1,p_2$

are the true proportions of cockroaches like these that would die within 48

hours on glass treated with diazinon and on plasterboard treated with diazinon,

respectively, check if the conditions for calculating a confidence interval for $p_1-p_2$are met.

Step by step solution

01

Given Information

It is given that $n_1=36$

$x_1=18$

$n_2=36$

$x_2=25$

02

Explanation

Conditions for hypothesis test are:

Random: As assigned arbitrarily, it is satisfied.

Independent: As used all values in population and used sample, it is satisfied.

Normal: Success in first sample is $18$and failures are $36-18=18$, both are greater than ten, it is satisfied.

All conditions are fulfilled, we can calculate confidence interval for$p_1-p_2$

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