A construction company is interested in testing the effectiveness of two types o

Question

A construction company is interested in testing the effectiveness of two types of dry wall patching methods. It has been reported that method 1 results in not being able to visually locate the patch 80% of the time ad that method 2 results in not being able to visually locate the patch 87% of the time. The company conducts a study in which method 1 is used in a random sample of 100 hole patches and method 2 is used in a different random sample of 100 hole patches. Upon inspection, 84 of the 100 holes patched with method 1 were not visible and 97 of the 100 holes patched with method 2 were not visible. What is p1hat - p2hat? (do not round)

Explanation / Answer

Here we have given that

method 1 : results in not being able to visually locate the patch 80 % of the time

method 2 : results not being able to visually locate the patch 87 % of the time

n1= size of the method 1 used random sample = 100

n2= size of the method 2 used random sample = 100

and

X1=holes patched with method 1 = 84

x2= holes patched with method 2 = 97

Now we want to find

P1hat = sample proportion of 1st sample= X1/ n

                                                                           = 84 / 100

                                                   P1hat =0.84

P2hat= sample proportion of 2nd sample = X2 / n

                                                                            = 97 / 100

                                                 P2hat = 0.97

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