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You are a researcher studying the lifespan of a certain species of bacteria. From a previous study, it was found that the standard deviation was 5.2 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.65 hours at a 99% level of confidence. What sample size should you gather to achieve a 0.65 hour margin of error? Round your answer up to the nearest whole number.

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JeanaShupp

Answer: 425

Step-by-step explanation:

As considering the given description, we have

Population standard deviation: [tex]\sigma=5.2[/tex]

Margin of error : E = 0.65

Critical value for 99% confidence interval : [tex]z_{\alpha/2}=2.576[/tex]

Formula to find the sample size : [tex]n=(\dfrac{z_{\alpha/2}\cdot \sigma}{E})^2[/tex]

i.e. [tex]n=(\dfrac{(2.576)\cdot (5.2)}{0.65})^2[/tex]

[tex]=(20.608)^2=424.689664\approx425[/tex]

Hence, the required minimum sample size =425

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