Question

The specification for the pull strength of a wire that connects an integrated circuit to its frame is 10 g or more. In a sample of 83 units made with gold wire, 70 met the specification, and in a sample of 115 units made with aluminum wire, 98 met the specification. Find a 99% confidence interval for the difference in the proportions of units that meet the specification between units with gold wire and those with aluminum wire.

Answer 1

Answer:

The formula for the lower and upper bounds for a confidence interval for the difference between to proportions is given in the picture.

In this case the p1 is going to be the proportion of units of gold wire that met the specification. p2 is going to be the proportion of aluminum wire that met the specification. The z for a 99% confidence interval is going to be 2. 575. n1 is going to be the total number of units of gold wire sampled and n2 is going to be the total number of units of aluminum wine sampled.

p1 = 70/83 = 0.843

p2 = 98/115 = 0.852

The difference between them is 0.009.

The value of the square root that is multiplying the z is: 0.052

The lower bound is going to be -0.043

the upper bound is going to be 0.061

The confidence interval is:

( -0.043, 0.061 )