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Fasteners are manufactured for an application involving aircraft. Each fastener is categorized either as conforming (suitable for its intended use), downgraded (unsuitable for its intended use but usable for another purpose), and scrap (not usable). It is thought that 85% of the fasteners are conforming, while 10% are downgraded and 5% are scrap. In a sample of 500 fasteners, 410 were conforming, 55 were downgraded, and 35 were scrap. Can you conclude that the true percentages differ from 85%, 10%, and 5%

Sagot :

Batolisisidn

Answer:

  • The true percentage actually differ from 85%, 10%, and 5%
  • chi-square statistic. = 5.0294

Step-by-step explanation:

85% of fasteners = conforming

10% of fasteners = downgraded

5% of fasteners = scrap

In a sample size of 500 fasteners

410 = conforming , 55 = downgraded,

The true percentage actually differ from 85%, 10%, and 5% as shown below

                               Observed Expected

conforming                 410                  500*0.85 = 425

Downgraded               55                  500*0.10 = 50

Scrap                            35                  500 * 0.05 = 25

Test statistic

determine the test statistic

= [ (410 - 425)2 / 425 + (55 -50)2 / 50 + (35 - 25)2 / 25 ]

chi-square statistic. = 5.0294

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