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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    

You might be interested in
The manufacturer of an airport baggage scanning machine claims it can handle an average of 560 bags per hour. (a-1) At α = .05 i
ioda

Answer:

The calculated value t = 1.76 < 2.131 at 0.05 level of significance

Null hypothesis is accepted

The manufacturer’s claim is greater than 560 bags per hour

Step-by-step explanation:

<u><em>Explanation</em></u>:-

Given sample size 'n' =16

Given the manufacturer of an airport baggage scanning machine claims it can handle an average of 560 bags per hour.

mean of the Population 'μ' = 560

Mean of the sample Χ⁻ = 538

sample standard deviation' S' = 50

<em><u>Null hypothesis</u></em><em>:H₀:μ > 560</em>

<em><u>Alternative Hypothesis</u></em><em>:H₁ : :μ < 560 (left tailed test)</em>

<em>Test statistic</em>

   t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }

  t = \frac{538-560 }{\frac{50}{\sqrt{16} } } = -1.76

|t| = |-1.76| = 1.76

<em>Degrees of freedom </em>

<em>γ = n-1 =16-1 =15</em>

t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } =t_{0.025} =2.131

<em><u>Conclusion</u></em>:-

The calculated value t = 1.76 < 2.131 at 0.05 level of significance

Null hypothesis is accepted

The manufacturer’s claim is greater than 560 bags per hour

6 0
3 years ago
How many 3 digit numbers can you make using these numbers: 4,2,9 (numbers can be reapeated)
bogdanovich [222]

Answer:

You can make 27 different 3 digit numbers

Step-by-step explanation:

Since we can use 3 different numbers this means that each of the 3 digits can be one of the 3 numbers (4,2,9). This means that there are 3 different values for the first digit, 3 different values for the second digit, and 3 different values for the third digit, which mean that we can make 3 x 3 x 3 different 3 digit numbers (we took the number of possible values for each digit and multiplied them together.

3 x 3 x 3 = 27

8 0
3 years ago
£140 is divided between Angad, Nick &amp; June so that Angad gets twice as much as Nick, and Nick gets three times as much as Ju
kramer

Answer:

84

Step-by-step explanation:

Let's say Nick gets amount N, Angad amount A, and June amount J.

Here's what we know:

A+N+J=140

A=2*N

N=3*J.

Let's plug these values in.

N=3*J, so A+N+J=140 can now be A+3*J+J=140.

A=2*N, and N=3*J, so A=2*3*J=6*J. Then, A+3*J+J=140 is now 6*J+3*J+J=140, so 10*J=140 and J=14. N = 3*J=42 and A=2*N=84. Checking this, 14+42+84=140, so we are good to go!

4 0
3 years ago
What is the measure of angle 3?
zheka24 [161]
Angles 6 and 8 add up to equal 180, so 2x - 5 + x + 5 = 180.  3x = 180 so x = 60.  Angle 3 is alternate interior to angle 6 which is 2(60) - 5 = 115, so angle 3 is also 115
7 0
3 years ago
Read 2 more answers
What is the surface area of the triangular prism shown​
Zigmanuir [339]
The surface area of the shape shown is 1008 square centimeters. I hope this helps!
3 0
3 years ago
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