A manufacturer finds that in a random sample of 100 of its CD players, 96% have no defects. The manufacturer wishes to make a claim about the percentage of nondefective CD players and is prepared to exaggerate. What is the highest rate of nondefective CD players that the manufacturer could claim under the following conditions? His claim would not be rejected at the 0.05 significance level if this sample data were used. Assume that a left-tailed hypothesis test would be performed.

This is what I did below but I got the wrong answer:

0.96 - 0.4 = 0.56

(0.4) (0.4) / 100 = 0.00016

Next I took the square root of 0.00016 and then divided

0.56/0.0126 = 44.4