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nadezda [96]
2 years ago
14

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. He wants to construct the 95

% confidence interval with a maximum error of 0.09 reproductions per hour. Assuming that the mean is 6.6 reproductions and the variance is known to be 4.84, what is the minimum sample size required for the estimate? Round your answer up to the next integer.
Mathematics
1 answer:
Fofino [41]2 years ago
7 0

Answer:

The minimum sample size is n = 2295    

Step-by-step explanation:

From the question we are told that

    The margin of error is  E = 0.09

    The sample mean is  \= x  = 6.6

     The variance is  \sigma^2 = 4.84

Generally the standard deviation is mathematically represented as

      \sigma  = \sqrt{\sigma^2}

=> \sigma  = \sqrt{4.84 }

=> \sigma  = 2.2

From the question we are told the confidence level is  95% , hence the level of significance is    

      \alpha = (100 - 95 ) \%

=>   \alpha = 0.05

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.96

Generally the sample size is mathematically represented as  

   n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2

=>   n = [\frac{1.96  *  2.2 }{0.09} ] ^2

=>   n = 2295    

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a) Median stays the same

b) Mean is decreased by $9

Step-by-step explanation:

The median is the number or the average of the two numbers that is in the middle of a sorted distribution of numbers,

Here the median number will be the 5th number counting from left or right from the sorted list of numbers. Therefor is is 891.

When 1027 is changed to 946 it will fall between 938 and 1002. So updated sorted list of numbers will now look like,

679, 715, 799, 844, 891, 917, 938, 946, 1002

Here also median will be the 5th number which will be equal to 891.

Therefore, , median will not change.

Mean is the value we get by taking the total value of the salaries and divide it by the number of employees.

In the initial case,

Mean =\frac{679+715+799+844+891+917+938+1002+1027}{9} =868

When the salary is changed from $1027 to $946,

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