Question

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 promotional 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

Answer 1

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