Find x and y. Special Triangle 30, 60, 90.

The 95% confidence interval for the difference between the mean yields for the two types of fertilizer is approximately 92.5536 pounds < < 35.39 pounds

Step-by-step explanation:

The harvest from each plot treated with fertilizer A and fertilizer B are presented as follows;

Fertilizer A

445, 510, 464, 472, 441, 480, 403, 460, 448, 457, 437, 505, 417

Fertilizer B

398, 380, 368 393, 424, 387, 378, 415

The number of trials of fertilizer A, n₁ = 13

The number of trials of fertilizer B, n₂ = 8

The confidence level = 95%

α = 1 - 0.95 = 0.05

∴ α/2 = 0.025

The degrees of freedom, df = 8 - 1 = 7

= 2.365

From Microsoft Excel, we get;

The standard deviation of the pounds of harvested fruits for the plots treated with fertilizer A s₁ = 30.71603

The mean of the pounds of harvested fruits for the plots treated with fertilizer A, = 456.8462

The standard deviation of the pounds of harvested fruits for the plots treated with fertilizer B s = 18.99201

The mean of the pounds of harvested fruits for the plots treated with fertilizer B,   = 392.875

The 95% confidence interval, C.I. for the difference between the mean yields for the two types of fertilizer can be constructed with the following formula

By variable substitution, we get;

The 95% confidence interval for the difference between the mean yields for the two types of fertilizer , which can be expressed as 92.5536 lbs. < < 35.39 lbs.