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

Suppose that customers assess door quality first interms of the ease of operation, followed by its durability. Thequality improvement team (QIT) might then assign an engineeringteam to determine the factors that contribute to these two mainproblems.

Smooth operation of a garage door is a critical qualitycharacteristic that affects both problems: If a door is too heavy,it’s difficult and unsafe to balance and operate; if it’s toolight, it tends to buckle and break down frequently or may notclose properly.

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

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

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

4.3 (2 points) What is the 95% confidenceinterval?

4.4 (2 points) What is the 99% confidenceinterval?

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