Question

Suppose a scientist is testing a antibiotics on a bacteria.
She does not look at its initial hourly growth rate "g", knowing it is in in a book somewhere.
She introduces the antibiotic and studies its growth over 25 hours, the scientist determines bacteria population adds 10,000 bacteria an hour with a std deviation of 3,000.
She now, retroactively, wants to know how big "g" needs to be in order to announce that her growth rate is lower at a 99% confidence level.

Answer 1

P(z<Z) table :

to announce that her growth rate is lower at a 99% confidence level :

P(z<Z) = 0.99

from table : Z = 2.33

SE = SD/(n^0.5) = 3000/(25^0.5) = 600

Z = 2.33

g = mean + 2.33*SE

= 10000 + 2.33*600

= 11398

g need to be atleast 11398 bacteria an hour

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