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lions [1.4K]
3 years ago
12

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.

Mathematics
1 answer:
kow [346]3 years ago
8 0

Complete Question

The complete question is shown on the first uploaded image

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

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