Question

Fertilizer: 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

10

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
523	464	483	460	491	403	484
448	457	437	516	417	420

Fertilizer B
362	414	408	398	382
368	393	437	387	373

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Part 1 of 3

Your Answer is correct

Explain why it is necessary to check whether the populations are approximately normal before constructing a confidence interval.

Since the sample size is ▼small, it is necessary to check that the populations are approximately normal.

Part 2 of 3

Your Answer is correct

Following are boxplots of these data. Is it reasonable to assume that the populations are approximately normal?

400 420 440 460 480 500 520 540

360 370 380 390 400 410 420 430 440 450

It ▼is reasonable to assume that the populations are approximately normal.

Part 3 of 3
Construct a  95% confidence interval for the difference between the mean yields for the two types of fertilizer. Let

μ1 denote the mean yield for fertilizer A. Use the TI-84 Plus calculator. Round the answers to one decimal place.

The 95% confidence interval for the difference between the mean yields for the two types of fertilizer is < μ1 - μ2< .

Answer 1

step 1

Since the sample size is small, it is necessary to check that the populations are approximately normal.

.the boxplots are

It is reasonable to assume that the populations are approximately normal.

step 3

using minitab>stat>basic stat>two sample test

we have

Two-Sample T-Test and CI: fertilizer A, Fertilizer B

Two-sample T for fertilizer A vs Fertilizer B

N Mean StDev SE Mean
fertilizer A 13 461.8 37.1 10
Fertilizer B 10 392.2 23.0 7.3

Difference = μ (fertilizer A) - μ (Fertilizer B)
Estimate for difference: 69.6
95% CI for difference: (41.7, 97.4)
T-Test of difference = 0 (vs ≠): T-Value = 5.19 P-Value = 0.000 DF = 21
Both use Pooled StDev = 31.8403

The 95% confidence interval for the difference between the mean yields for the two types of fertilizer is 41.7< μ1 - μ2<97.4 .