Question

The percentage of cracked tile is an important standard for construction companies producing tiles. Two samples of tile are collected from two buildings with the following information:

Building (1): 6000 tiles tested for cracks and 406 cracked tiles found.

Building (2): 2000 tiles tested for cracks and 83 cracked tiles found.

(a) What is the proportion of non-conforming tiles in each sample?

(b) What is the 99% confidence interval for the difference of proportion of non-conforming tiles in sample (1) and (2)?

(c) We have the information that the resin mixture used in building (1) is different than the one used in building (2). Using the results from part (b), can we conclude that the resin mixture in building (1) is better that the one in building (2)? Explain.

Answer 1

a)

proportion of non-conforming tiles (1)=406/6000=0.0677

proportion of non-conforming tiles(2)=83/2000=0.0415

b)

99% confidence interval for difference in proportions

=(0.0677-0.0415)+/-2.576*sqrt((0.0677*(1-0.0677)/6000)+(0.0415*(1-0.0415)/2000))

=0.0262+/-0.0142

=(0.0120, 0.0404)

c)As,both limits are positive,we can conclude that the resin mixture in building (1) is better that the one in building (2).