Question

It is common for researchers to struggle with how large to make their sample. A plant biologist uses soybeans as test subjects. Soybean plants are treated with an experimental herbicide, then their overall health and yield is monitored for several months. At the end of the experiment, each soybean plant is harvested and further analyzed. The analysis of each individual plant gives one data point for the study. Why might a researcher want a large sample size?

i. Increasing the sample size reduces the population standard deviation.

ii. Increasing the sample size increases the population standard deviation.

ii. Increasing the sample size produces a narrower confidence interval.

iv. Increasing the sample size produces a wider confidence interval.

v. Increasing the sample size gives a higher confidence level.

Answer 1

CI = mean +/- z*sigma/sqrt(n)

as we can see increasing the value of n reduces the second term which in turn narrows the CI

iii. Increasing the sample size produces a narrower confidence interval.