Question

Bags of pretzels are sampled to ensure proper weight. The overall average for the samples is 9 ounces. Each sample contains 25 bags. The standard deviation is estimated to be 3 ounces. The upper control chart limit (for 99.7% confidence) for the average would be ________ ounces.

Answer 1

Answer:

The value is $UCL = 10.8$  

Step-by-step explanation:

From the question we are told that

    The sample mean is  $\= x = 9 \ ounce$

    The sample size is  n =  25

    The standard deviation is  $\sigma = 3 \ ounce$

Given that the sample size is not large enough i.e  n<  30  we will make use of the student t distribution table  

From the question we are told the confidence level is  99.7% , hence the level of significance is    

      $\alpha = (100 -99.7 ) \%$

=>   $\alpha = 0.003$

Generally the degree of freedom is  $df = n- 1$

=>  $df = 25 - 1$

=>  $df = 24$  

Generally from the student t distribution table the critical value  of  $\frac{\alpha }{2}$ at a degree of freedom of $df = 24$   is  

   $t_{\frac{\alpha }{2} , 24 } = 3.0$

Generally the margin of error is mathematically represented as  

      $E = t_{\frac{\alpha }{2} , 24} * \frac{\sigma }{\sqrt{n} }$

=>     $E = 3.0 * \frac{3 }{\sqrt{25} }$

=>     $E =1.8$

Gnerally the  upper control chart limit  for 99.7% confidence is mathematically represented as

         $UCL = \= x + E$

=>      $UCL = 9 + 1.8$  

=>      $UCL = 10.8$