Question

In an agricultural experiment, the effects of two fertilizers on the production of limes were measured. Eighteen randomly selected plots of land were treated with a brand new fertilizer, and 11 randomly selected plots were treated with an old fertlizer. The number of pounds of harvested limes were measured from each plot. The results are given below. (Round answers to two decimal places.)

New Fertilizer   Old Fertilizer
469   419
482   442
481   436
485   425
482   424
476   435
473   431
461   440
481   449
477   440
477   409
468  
492  
468  
468  
501  
473  
481  

Find a 93% confidence interval for the difference between the mean weight of the harvested limes.

margin of error:
lower limit:
upper limit:


Based on the results, is the new fertilizer better than the old fertilizer?

• No, we are 93% confident that new fertilizer is not better than old fertilizer.
• Yes, we are 93% confident that new fertilizer is better than old fertilizer.
• It's not clear if the new fertilizer is better than the old fertilizer.

Answer 1

using excel>addin>phstat>two sample test

we have

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0		for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample			Data
Sample Size	18		Confidence Level	93%
Sample Mean	477.5
Sample Standard Deviation	9.562487985		Intermediate Calculations
Population 2 Sample			Degrees of Freedom	27
Sample Size	11		t Value	1.8867
Sample Mean	431.8181818		Interval Half Width	7.4936
Sample Standard Deviation	11.63458793
			Confidence Interval
Intermediate Calculations		Interval Lower Limit	38.1882
Population 1 Sample Degrees of Freedom	17		Interval Upper Limit	53.1754
Population 2 Sample Degrees of Freedom	10
Total Degrees of Freedom	27
Pooled Variance	107.7088
Standard Error	3.9718
Difference in Sample Means	45.6818
t Test Statistic	11.5014
Two-Tail Test
Lower Critical Value	-2.0518
Upper Critical Value	2.0518
p-Value	0.0000
Reject the null hypothesis

margin of error: 7.49
lower limit: 38.19
upper limit:53.18


Based on the results, is the new fertilizer better than the old fertilizer?

• Yes, we are 93% confident that new fertilizer is better than old fertilizer.