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AfilCa [17]
4 years ago
7

A sample of 900 computer chips revealed that 75% of the chips do not fail in the first 1000 hours of their use. The company's pr

omotional literature claimed that above 72% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to support the company's claim
Mathematics
1 answer:
Vaselesa [24]4 years ago
8 0

Answer:

No the evidence is not sufficient

Step-by-step explanation:

From the question we are told that

    The  sample  size is  n  =  900

   The  sample  proportion is  \r p  = 0.75

    The  population proportion is  p  = 0.72

The  Null hypothesis is

   H_o  : p =  0.72

The  Alternative  hypothesis is

   H_a  :  p > 0.72

The level of significance is given as  \alpha  = 0.05

The critical value for the level of significance is  t_{\alpha }  =  1.645

 Now the test statistic is mathematically evaluated as

          t =  \frac{\r p -  p }{ \sqrt{\frac{p(1-p)}{\sqrt{n} } } }

substituting values

        t =  \frac{ 0.75 -  0.72 }{ \sqrt{\frac{0.72 (1-0.72)}{\sqrt{900} } } }

        t =  0.366

Since the critical value is  greater than the test statistics then the Null hypothesis is rejected which there is no sufficient evidence to support the claim

       

 

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