A plant scientist wishes to know the average nitrogen uptake of a vegetable crop. A pilot study ...

  

A plant scientist wishes to know the average nitrogen uptake of a vegetable crop. A pilot study showed that the standard deviation of the uptake is about 120 ppm. The scientist will use this information to design her study.

a) The scientist wishes to be 90% confident in knowing the true mean within 20 ppm. What is the required number of plants for her sample?

b) The scientist changes her mind and decides she wants to be 95% confident that she will capture the true mean within 20 ppm. How does this change her sample size?

c) Suppose the scientist’s boss tells her they can only afford a sample size of 90. What confidence level will she be using if she wants to know the true mean within 20ppm?

d) Given the scientist is limited to a sample size of 90 and her boss insists on a 90% confidence interval, what margin of error must she use?