Question

Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the p-value is

Answer 1

Answer:

The value is  $p- value = 0.041815$

Step-by-step explanation:

From the question we are told that

  The  population mean is $\mu = 40 \ hours$

  The  sample size is  $n = 18$

    The  sample mean is  $\= x = 37.8 \ hours$

   The standard deviation is  $\sigma = 5.4\ hours$

The null hypothesis is  $H_o : \mu = \ge 40$

The alternative hypothesis is  $H_a : \mu < 40 \ hour s$

Generally the test statistic is mathematically evaluated as

       $t= \frac{\= x - \mu}{ \frac{\sigma}{ \sqrt{n} } }$

      $t= \frac{37.8 - 40}{ \frac{5.4}{ \sqrt{18 } }$

      $t= -1.73$

From the z - table the p-value is obtained and the value is  

      $p- value = P(Z < -1.73)$

        $p- value = 0.041815$