Question

A manufacturing company uses two different machines, A and B, each of which produces a certain item part. The number of defective parts produced by each machine is about 1 percent. Suppose two independent random samples, each of size 100, are selected, where one is a sample of parts produced by machine A and the other is a sample of parts produced by machine B. Which of the following is true about the sampling distribution of the difference in the sample proportions of defective parts?

A The mean is 0 and the distribution is approximately normal
B The mean is 0 and the distribution will not be approximately normal
C The mean is 0.01 and the distribution is approximately normal
D The mean is 0.01 and the distribution will not be approximately normal.
Ε The mean is 1 and the distribution is approximately normal.

Answer 1

The sampling distribution of the difference in the sample proportions of defective parts is approximately normal with a mean of 0.01.

Step-by-step explanation:

The sampling distribution of the difference in the sample proportions of defective parts can be approximated by a normal distribution. The mean of the sampling distribution is equal to the difference in the population proportions, which is 0.01. This means that on average, machine A produces 1% more defective parts than machine B.

Therefore, the correct answer is option D. The mean is 0.01 and the distribution will not be approximately normal.

Answer 2

B: The mean is 0 and the distribution will not be approximately normal

Step-by-step explanation:

It is true that the mean is 0 because it is the difference in the population proportions, 0.01−0.01. However, normality cannot be assumed because the sample sizes are not large enough.