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

Question

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.

Calculate a 95% confidence interval for the true mean DNA concentration on the ocean floor. (3pts)

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

we know that the confidence interval is given as

mean +- z* SD/sqrt(N) , where z = 1.96 for 95% CI from the z table n = 30 , mean = 0.31 and sd = 0.15

putting the values in the above equation and solving we get

0.31 +- 1.96*0.15/sqrt(30)

= 0.256, 0.363

if the sample size is reduced to 15 we can again calculate the CI

0.31 +- 1.96*0.15/sqrt(15)

0.234, 0.385 , so the CI becomes wider

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