In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Thirteen randomly selected plots of land were treated with fertilizer A, and 8 randomly selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured from each plot. Following are the results. 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

Required:
Construct a 95% confidence interval for the difference between the mean yields for the two types of fertilizer.

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.

answer is 12345678900987654321234567890987654321

step-by-step explanation: