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Karo-lina-s [1.5K]
3 years ago
15

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 13.6

reproductions and the population standard deviation is known to be 1.9. If a sample of 189 was used for the study, construct the 85% confidence interval for the true mean number of reproductions per hour for the bacteria. Round your answers to one decimal place.
Mathematics
1 answer:
dimaraw [331]3 years ago
5 0

Answer:

The confidence interval is  13.4<  \mu < 13.8

Step-by-step explanation:

From the question we are told that

   The sample  mean is \= x  =  13.6

     The standard deviation is \sigma =  1.9

     The sample  size is  n  =  189

given that the confidence level is  85% then the level of significance is mathematically represented as

            \alpha = (100 - 85 )\%

            \alpha  =  0.15

Next we obtain the critical value  of \frac{\alpha }{2} from the normal distribution table  the value  is  

      Z_{\frac{\alpha }{2} } =  1.44

Generally the margin of error is mathematically represented as

        E =  Z_{\frac{\alpha }{2} } *  \frac{\sigma}{\sqrt{n} }

=>     E = 1.44*  \frac{1.9}{\sqrt{189} }

=>     E = 0.1990

The  85%  confidence interval is mathematically represented as  

        \= x  - E <  \mu

=>      13.6- 0.1990 <  \mu <  13.6+ 0.1990

=>      13.4<  \mu < 13.8

           

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