In 2013 researcher Kandy Rojas conducted an economic analysis of foliar fungicides used in Northeast Texas wheat production. She obtained winter wheat (Triticum aestivum L.) data on fungicide treatment, location, yield, and disease severity for four soft-red winter wheat cultivars (Magnolia, Terral LA841, Pioneer 25R47, Coker 9553) from the Texas A&M AgriLife Extension Representative in Commerce, TX. The wheat dataset that can be found in the eCollge website for the course contains selective data for year 2012 from Rojas (2013). The variable location (loc) equals 1 if Leonard, 2 if Royse City, and 3 if Howe; the variable replication (rep) is the replication of the experiment on the subjects (fungicide application, treated versus non-treated, on winter wheat plants) and there were 6 replications per cultivar per location, per year; the variable variety also called cultivar (var) equals 1 if Cooker 9553, 2 if Magnolia, 3 if Pioneer 25R47, and 4 if Terral LA841; the variable treatment equals 1 if treated (sprayed with the foliar fungicide TebuStar 3.6L at 280 g/ha and diluted in 93 liters of water per hectare) and 0 if non-treated (non-sprayed); the variable yield is wheat yield in kg/ha; and the variable wheat price (wprice) is the wheat price in $/kg.

Table 1. Yield per cultivar, averaged across locations and treatments in 2012.

	Yield (kg/ha)
Cultivar	n	Mean	Std. Dev.
Coker 9553	37	6407.7	580.10
Terral LA841	37	5706.9	588.62
Magnolia	37	6035.9	504.97
Pioneer 25R47	37	5890	1052.74
Overall

3. Table 2 below summarizes yield in 2011 (rather than in 2012). Use Tables 1 and 2 to test the hypothesis that wheat yield changed. That is, test the hypothesis that wheat yield is different from the yield levels specified in Table 2 below. In each of the five t tests:

c. Type the formula. Make sure you provide the formula in each t test. (Points: 1)

d. Type the procedure. (Points: 4)

e. Type the final answer. (Points: 3)

f. Type the critical value(s). Use = 0.05 significance level. (Points: 1)

g. State the correct conclusion ("There is sufficient evidence at the = 0.05 significance level to support..." or "There is NOT sufficient evidence at the = 0.05 significance level to support..."). Make sure you state the conclusion in terms of H₁. (Points: 3)

Table 2. Yield per cultivar, averaged across locations and treatments in 2011.

Wheat Yield in 2011
Cultivar	Mean (kg/ha)
Coker 9553	4,974.75
Terral LA841	4,604.81
Magnolia	4,250.59
Pioneer 25R47	4,698.27
Overall	4,632.10

Which formula do they mean for question 3c? The one for population, Z score?