Question

Explain why the conditions for using two-sample z procedures to perform inference about $p1-p2$are not met in the settings

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. Breaks start as hairline cracks called “checking.” Assign $65$newly baked crackers to the microwave and another $65$to a control group that is not microwaved. After one day, none of the microwave group and $16$ of the control group show checking.^$8$

Short answer

From the given information,

The success rate in the first sample, i.e. the microwave group, is $0$(less than $10$). It means that the normalcy assumption isn't met in this case.

As a result, the two-proportion z-test is inappropriate in this situation.

Step-by-step solution

Given Information

It is given in the question that, the values are$x_1=0,n_1=65,x_2=16,n_2=65$

Step 2: Explanation

The number of successes in both samples must be greater than $10$to execute the two-proportion z-test.

The success rate in the first sample, i.e. the microwave group, is $0$(less than $10$). It means that the normalcy assumption isn't met in this case.

As a result, the two-proportion z-test is inappropriate in this situation.