Question

An agricultural economist wants to know if the average number of plants grown differs for two different fertilizers, which we will call Fertilizer 1 and Fertilizer 2. He samples 45 plants from a field sprayed with Fertilizer 1 and 45 plants from a field sprayed with Fertilizer 2. The sample standard deviations are 4 and 1, respectively. What test should be conducted and with what degrees of freedom? (For the degrees of freedom, assume the agricultural economist does not have access to a calculator nor software). More than one answer may be correct.

	a.	pooled t-test, df = 89
	b.	matched-pairs t-test, df = 44
	c.	pooled t-test, df = 88
	d.	two-sample t-test, not pooled, df = 44
	e.	two-sample t-test, not pooled, df = 88

Answer 1

Answer:

d. two-sample t-test, not pooled, df = 44

Explanation:

For the comparison of the two population means, we need to use the two sample t test. We are not given that the population standard deviations or variances are equal, so we use not pooled t test. For finding degrees of freedom for this test, we use conservative degrees of freedom method. We use degrees of freedom as minimum of (n1 - 1, n2 - 1) for this test. So, df = min(45 - 1, 45 - 1) = min(44, 44) = 44.