Question

Broken crackers We don’t like to find broken crackers when we open the package. How can makers reduce breaking? One idea is to microwave the crackers for $30$seconds right after baking them. Randomly assign $65$newly baked crackers to the microwave and another $65$to a control group that is not microwaved. After $1$day, none of the microwave group were broken and $16$of the control group were broken. Let $p_1$be the true proportions of crackers like these that would break if baked in the microwave and $p_2$be the true proportions of crackers like these that would break if not microwaved. Check if the conditions for calculating a confidence interval for$p_1-p_2$met.

Short answer

It is not suitable to find confidence interval for$p_1-p_2$

Step-by-step solution

Given Information

It is given that $n_1=65$

$x_1=0$

$n_2=65$

$x_2=16$

Explanation

Testing three conditions for hypothesis test:

Random: As they are assigned, it is satisfied.

Independent: Since all data values in population and used sample, this condition is satisfied.

Normal: There are zero success in first sample, it is not at least $10$.

As normal condition is not met, we cannot find confidence interval$p_1-p_2$