Question: Two brands of refrigerators, A and B, are guaranteed for one year. In a random sample of 100 refrigerators of brand A, 24 were observed to fail before the guarantee period ended. A random sample of 120 brand B refrigerators also revealed 24 failures during the guarantee period.

(a) Estimate the true difference between population proportions of failures during the guaranteed period with a confidence of 95%.

(b) Is there a discernible difference between these two brands?

(c) Please explain your response.