Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 420 gram setting. It is believed that the machine is underfilling the bags. A 49 bag sample had a mean of 413 grams. Assume the population variance is known to be 676 . A level of significance of 0.1 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

Answer 1

Answer:

The  value is  $p-value = 0.0297$

Step-by-step explanation:

From the question we are told that

   The population mean is  $\mu = 420 \ g$

   The The  sample  size is $n = 49$

    The sample  mean is  $\= x = 413 \ g$

    The  population variance is   $\sigma^2 = 676$

Generally the population standard deviation is  mathematically represented as

     $\sigma = \sqrt{\sigma^2 }$

     $\sigma = \sqrt{676}$

     $\sigma = 26$

The null hypothesis is  $H_o : \mu = 420 \ g$

The  alternative  hypothesis is $H_a : \mu < 420 \ g$

 Generally the test statistics is mathematically represented as

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

=>        $z= \frac{ 413 - 420 }{ \frac{ 26 }{\sqrt{49} } }$

=>       $z = -1.884$

The  p-value is  obtained from the z-table table and the value is  

       $p-value = P(Z < -1.885) = 0.029715$

       $p-value = 0.0297$