Question

You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 25 bacteria reveals a sample mean of ¯x=70x¯=70 hours with a standard deviation of s=5.6s=5.6 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.6 hours at a 90% level of confidence.

What sample size should you gather to achieve a 0.6 hour margin of error? Round your answer up to the nearest whole number.

n =   bacteria

Answer 1

margin of error of 0.6 hours

E = 0.6

90% level of confidence.

c = 90% = 0.90

a standard deviation of s=5.6 hours

Use s as an estimate of population SD

= 5.6

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05 and 1- /2 = 0.950

Search the probability 0.950 in the Z table and see corresponding z value

  = 1.645   

Now, sample size (n) is given by,

= {(1.645* 5.6 )/ 0.6 }²

=  235.724844444

= 236 ..(round to the next whole number)

n = 236  bacteria