1. Outside living cells, DNA mainly occurs on the ocean floor, where it plays an

Question

1. Outside living cells, DNA mainly occurs on the ocean floor, where it plays an important role in nourishing seafloor life. The DNA concentrations from a random sample of 30 ocean floor specimens were found to have an approximately normal distribution with mean of 0.31 g/m2 and a standard deviation of 0.15 g/m2.

a. Calculate a 95% confidence interval for the true mean DNA concentration on the ocean floor.

b. Assuming that you held everything else constant, would the width of the confidence interval become wider, narrower, or stay the same if your sample was half the size?

Explanation / Answer

here we can do this by t distribution as well with z distribution; cause in some books for sample size 30 we can use z distribution. Though we should use t distribution when population std deviation not known unless size is very large

here std error of mean =std deviation/(n)1/2 =0.15/(30)1/2 =0.0274

a) from t distribution:

for 95% CI and (n-1=29) degree of freedom ; critical value of t =2.045

hence 95% confidence interval for the true mean DNA concentration on the ocean floor =sample mean -/+t*std error

=0.31 -/+ 2.045*0.0274 =0.2540 to 0.3660

from z distribution

for 95% CI ;critical value of z =1.96

95% confidence interval for the true mean DNA concentration on the ocean floor =sample mean -/+z*std error

=0.31 -/+ 1.96*0.0274 =0.2563 to 0.3637

b)

as we have seen that std error of mean is inversely propotional to square root of sample size,

hence as sample size reduced to half ; std error will increase and therefore margin of error increase and will give

wider width of the confidence interval

please revert for any clarification required

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