Crop researchers plant 15 plots with a new variety of corn. the yields in bushels per acre are: 138.0 139.1 113.0 132.5 140.7 109.7 118.9 134.8 109.6 127.3 115.6 130.4 130.2 111.7 105.5 assume that bushels per acre. a) find the 90% confidence interval for the mean yield for this variety of corn. b) find the 95% confidence interval. c) find the 99% confidence interval. d) how do the margins of error in (a), (b), and (c) change as the confidence level increases?

There is a relationship between confidence interval and standard deviation:

Where is the mean, is standard deviation, and n is number of data points.
Every confidence interval has associated z value. This can be found online.
We need to find the standard deviation first: 

When we do all the calculations we find that:

Now we can find confidence intervals:

We can see that as confidence interval increases so does the error margin. Z values accociated with each confidence intreval also get bigger as confidence interval increases.
Here is the link to the spreadsheet with standard deviation calculation:
https://docs.google.com/spreadsheets/d/1pnsJIrM_lmQKAGRJvduiHzjg9mYvLgpsCqCoGYvR5Us/edit?usp=sharing