Question

Compute a 99% confidence interval for the mean weight of toxic substance per gram of mold culture. State the assumption you make about the population.

Answer 1

Complete Question

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Answer:

The  99% confidence interval is  $2.4309 < \mu < 4.9328$

Step-by-step explanation:

From the question we are told that

   The data is   3, 2,5, 3, 2, 6, 5,4.5, 3, 3, and 4

    The sample size is  n  =  11

Generally the sample mean is mathematically represented as

     $\= x = \frac{\sum x_i}{n}$

=>  $\= x = \frac{3+ 2+5+ \cdots +4 }{11}$

=>  $\= x = 3.6818$

Generally the sample standard deviation  is mathematically represented as

    $\sigma = \sqrt{\frac{\sum [ x_i - \= x ] }{n} }$

=>  $\sigma = \sqrt{\frac{[ 3 - 3.6818 ]^2 +[ 2 - 3.6818 ]^2 + \cdots + [ 4 - 3.6818 ]^2 }{11} }$

=>  $\sigma = 1.3091$

Given that the confidence interval is 99% then the level of significance is mathematically represented as

         $\alpha= (100 - 99) \%$

=>      $\alpha= 0.01$

Given  that the sample size is small we will making use of t distribution table  

Generally from the t distribution table the critical value  of   at a degree of freedom of  is  

   $t_{\frac{\alpha }{2} , 10 } =3.16927267$

Generally the margin of error is mathematically represented as  

      $E = 3.16927267 * \frac{1.3091 }{\sqrt{11} }$

     $E = 1.251$

Generally 99% confidence interval is mathematically represented as  

      $3.6818 -1.251 < p < 3.6818 + 1.251$

=>    $2.4309 < \mu < 4.9328$