A farmer decides to try out a new fertilizer on a test plot

A farmer decides to try out a new fertilizer on a test plot containing 10 stalks of corn. Before applying the fertilizer, he measured the height of each stalk. Two weeks later (after applying the fertilizer), he measures the skills again, being careful to match each stalk\'s new height to its previous one. The results are as follows: Find a 95% confidence interval for the increase in stalks height due to fertilizer (assume normality for the population).

Solution

standard error of mean = Z(critical ) * standard deviation/sqrt(n)

= 1.96 * 1.9479/sqrt(10)

= 1.207

confidence interval = mean +/- standard error of mean

= 7.36 + / - 1.207

hence 95% confidence interval is 6.15 < mean < 8.57

stalk	1	2	3	4	5	6	7	8	9	10
Before	35.5	31.7	31.2	36.3	22.8	28	24.6	26.1	34.5	27.7
After	45.3	36	38.6	44.7	31.4	33.5	28.8	35.8	42.9	35
Difference(X)	9.8	4.3	7.4	8.4	8.6	5.5	4.2	9.7	8.4	7.3
SUM(X)	73.6
mean	7.36
(mean-X)^2	5.9536	9.3636	0.0016	1.0816	1.5376	3.4596	9.9856	5.4756	1.0816	0.0036
SUM((mean-X)^2)	37.9440
variance	3.7944
standard deviation	1.9479