Question

A farmer decides to try out a new fertilizer on a test plot containing 10 stalks of corn. Before applying the fertilizer, he measures the height of each stalk. Two weeks later, after applying the fertilizer, he measures the stalks again. He compares the heights of these stalks to 10 stalks that did not receive fertilizer. Did the fertilizer help? Use a significance level of 0.10 to test whether the height of the stalks increased.

The differences are calculated and the mean difference is found to be -1.18 inches with a standard deviation of 1.05 inches. Set up the appropriate hypothesis test and find the standardized test statistic and P-value.

Answer 1

The test statistic is

   

   

df = 10 - 1 = 9

P-value = P(T < -3.554)

             = 0.0031

Since the P-value is less than the significance level(0.0031 < 0.10), so we should reject the null hypothesis.

At 0.10 significance level, there is sufficient evidence to conclude that the height of the stalks has increased by applying the fertilizer.