The data for this problem is in the 'variety trial data.xlsx' file available . An agronomist chooses 10 sites to trial two new varieties of wheat. At each site he chooses a single plot (same size at every site) and then divides it evenly into two. One side of each plot is randomly chosen for variety 1 and the other is used for variety 2. At the end of the season, each of the 20 subplots is harvested and the yield per hectare recorded in the 'variety trial data.xlsx' file.

The agronomist wants to know whether there is a real difference in yield between the varieties.

What would be the best statistical test to use?

Carry out the test. What is the p-value given by the test? Can we conclude there a real difference in yield between the varieties? Based on the 95% confidence interval, what would we say is a reasonable lower bound on the difference between the yields of the two varieties? Which variety would we expect to yield more?

The next season a similar trial is conducted at a much larger number of sites. The data from this trial is found in the 'variety trial data.xlsx' file as well.

How many trial sites were used for the trial this time?

Sadly, there is an outbreak of a fungal disease across the trial region that badly affects some of the trial sites. The agronomist decides to only use any site where the mean yield for the site is more than 30% of the average yield for all the sites (ie sites that were less than 30% of average were scrapped). (Note, the mean yield for the site is the average of the yields for the two varieties at that site).

What could be the subset of the data that fit the criteria. How many trial sites should be retained? (You may subsetting in R or in Excel as you prefer.)

Carry out the test for difference on this subset of sites. What is the p-value given by the test this time? Can we conclude there a real difference in yield between the varieties?

this.is.the.data.from.the.first.variety.trial X X.1 1 2 3 4 5 site var 1 var 2 6 1 5.5 8.4 7 2 6.3 7.3 8 3 5.3 7.8 9 4 6.9 7.3 10 5 6.3 7.2 11 6 3.6 6.1 12 7 6.9 7.9 13 8 4.8 5.8 14 9 4.8 6.8 15 10 5.5 6.7

It would be greatly appreciated if the command to enter in R is also provided to get the answers. Cheers!