A certain company makes three grades (A, B, and C) of a particular electrical component. Historically, grade A components have a 2 percent defective rate, grade B components have a 5 percent defective rate, and grade C components have a 10 percent defective rate. Since grade A components are less likely to be defective, the company can charge more money for those components than it can charge for the grade B or C components. Similarly, the company can charge more money for grade B components than it can charge for grade C components. Recently, the company found a batch of components in a warehouse that were known to be of the same grade, but the grade was not labeled on the components. To determine the grade (A, B, or C), the company selected from that batch a random sample of 200 components, which contained 16 defective components.
a) Construct and interpret a 95 percent confidence interval for the proportion of defective components in the batch.
b) Does the interval calculated in part (a) allow the company to clearly determine the grade of component that was produced in the batch

Phase 1: Identifies a reasonable confidence period with both the title or form and checks suitable conditions. one z-interval test, p, that true percentage of defective parts in such a lot of Clauses:

1. Unique component sampling

2. This survey size is enough, to the fact to conclude the composition of that percentage of a sample was roughly natural, which the amount for successes and the number of losses are either greater than 10 (or 5 or 15). Needs to check: A 200-component representative selection of a big batch was picked. Each has far more than 15 achievements or failures (16 and 184).

Phase 2: Mechanisms Correct Pick problems for Pink and Blue it Committee of a College. Similar products are part of the program of a College Board. It is prohibited for such resources to be used and distributed online or in a printed form far beyond the participation of the college in the package, which leads to intervals (0.0424, 0.1176).

Phase 3: Background analysis In just this study, we consider 95% of its computed value to have between 4.24% and 11.76% for both the real number of defective components within the batch.

In part (b):

Its standard deviation of 95 percent found in Part (a) allows a company to eliminate class A as its 2 percent faulty rate is not among the computed value within this interval. It period however does not enable the company to decide between levels B and C, since the two faulty rates (5% and 10%) were examined.

Scoring: In 4 components the question is rated. Section 1 comprises part (a) step 1; part (a) or step 2 comprises of the part (a), part (3), part (a), and part (4) (b). The part was marked as correct (E), partly right (P) (I).