Question

4. Overhead Door (OD) Corporation’s founder, C. G. Johnson, invented the upward-lifting garage door in 1921 and the electric garage door opener in 1926. Since then OD has been a leading supplier of commercial, industrial, and residential garage doors sold through a nationwide network of more than 450 authorized distributors. They have built a solid reputation as a premier door supplier, commanding 15 % share of the market.

Suppose that customers assess door quality first in terms of the ease of operation, followed by its durability. The quality improvement team (QIT) might then assign an engineering team to determine the factors that contribute to these two main problems.

Smooth operation of a garage door is a critical quality characteristic that affects both problems: If a door is too heavy, it’s difficult and unsafe to balance and operate; if it’s too light, it tends to buckle and break down frequently or may not close properly.

Suppose the design engineers determine that a standard garage door should weigh a minimum of 74 kg. and a maximum of 86 kg., which thus specifies its design quality specification. QIT is inspecting if there is evidence that the percentage of defective doors does not exceed 7%. Suppose the QIT decides to collect data on the actual weights of 60 standard garage doors sampled randomly from their monthly production of almost 2,000 doors. See the tables on the next page.

4.1 (2 point) What is the sample defective rate ?

4.2 (2 points) Formulate and test an appropriate set of hypotheses to determine if the machine can be qualified. Use α = 0.05. Find the P-value.

4.3 (2 points) What is the 95% confidence interval?

4.4 (2 points) What is the 99% confidence interval?

Table 2:

T\D	1	2	3	4	5	6	7	8	9	10
9	81	82	80	74	75	81	83	86	88	82
1	73	77	83	81	76	76	82	83	79	84
5	85	78	76	81	82	83	76	82	86	79

T\D	11	12	13	14	15	16	17	18	19	20
9	80	78	84	75	84	78	77	79	84	84
1	80	84	82	83	75	81	78	85	85	80
5	76	76	78	72	84	76	74	85	82	79

Answer 1