Question

NarStor, a computer disk drive manufacturer, claims that the median time until failure for their hard drives is more than 14,400 hours. You work for a consumer group that has decided to examine this claim. Technicians ran 16 NarStor hard drives continuously for almost three years. Recently the last drive failed. The times to failure (in hours) are given in the following table. Give the test statistic.330 620 1870 2410 4620 6396 7822 81028309 12882 14419 16092 18384 20916 23812 25814

Answer 1

Answer:

The test statistics is  $t = -1.727$

Step-by-step explanation:

From the question we are told that

The data given is  

   330 620 1870 2410 4620 6396 7822 81028309 12882 14419 16092 18384 20916 23812 25814

 The population mean is  $\mu = 14400$

    The  sample  size is  n =  16

  The  null hypothesis is  $\mu \le 14400$

    The  alternative hypothesis is  $H_a : \mu > 14400$

The sample mean is mathematically evaluated as

  $\= x = \frac{\sum x_i}{n}$

So

   $\= x = \frac{330+ 620+ 1870 +2410+ 4620+ 6396+ 7822+ 8102+8309+ 12882+ 14419+ 16092+ 18384 +20916+ 23812+ 25814 }{16}$

=>  $\= x = 10799.9$

The  standard deviation is mathematically represented as

      $\sigma =\sqrt{\frac{ \sum (x_i - \=x)^2}{n}}$

So

$\sigma =\sqrt{\frac{(330- 10799.9)^2 + (620- 10799.9)^2+ (1870- 10799.9)^2 +(2410- 10799.9)^2 + (4620- 10799.9)^2 +(6396- 10799.9)^2 +(7822- 10799.9)^2 }{16}} \ ..$

   $..\sqrt{ \frac{(8102 - 10799.9)^2 +(8309 - 10799.9)^2 + (12882 - 10799.9)^2 + (14419 - 10799.9)^2 + (16092 - 10799.9)^2 + (18384 - 10799.9)^2 +(20916 - 10799.9)^2 }{16}} \ ...$

  $\ ... \sqrt{\frac{(23812 - 10799.9)^2 +(25814 - 10799.9)^2 }{16}}$

=>  $\sigma = 8340$

  Generally the test statistic is mathematically represented as

  $t = \frac{10799.9- 14400}{ \frac{8340}{\sqrt{16} } }$

$t = -1.727$

From the z-table  the p-value is  

     $p-value = P(Z > t) = P(Z > -1.727) = 0.95792$

 From the values obtained we see that

        $p-value > \alpha$  so we fail to reject the null hypothesis

Which implies that the claim of the NarStor is wrong