Question

W75A - Please answer in detail using EXCEL Function

T-test of 2 means (Similar to presentation in class; but in a different context)

              (Wednesday class)

              Researchers in Georgia take a sample of diameters from 30 old-growth pine trees growing on two separate and adjoining tracts of land, labeled north and south, to see if the trees are identical.   The data are shown in the Tables below and reproduced in the Excel answer workbook.

1. Using Excel’s t-test of two means, calculate the P-value of a two-tail taste to identify whether the mean tree diameter from the north tract and south tracts are identical or not at a 5% level of significance. (Round to four digits.) Make sure you state the null and alternative hypotheses, as well as a formal conclusion to your test. (The Excel answer workbook reminds you to do so!) Assume variances (and, therefore, standard deviations are not equal. (1 point)

(North)

27.8	14.5	39.1	3.2	58.8	55.5	25	5.4	19	30.6
15.1	3.6	28.4	15	2.2	14.2	44.2	25.7	11.2	46.8
36.9	54.1	10.2	2.5	13.8	43.5	13.8	39.7	6.4	4.8

              (South)

44.4	26.1	50.4	23.3	39.5	51	48.1	47.2	40.3	37.4
36.8	21.7	35.7	32	40.4	12.8	5.6	44.3	52.9	38
2.6	44.6	45.5	29.1	18.7	7	43.8	28.3	36.9	51.6

Answer 1

Data

North	South
27.8	44.4
14.5	26.1
39.1	50.4
3.2	23.3
58.8	39.5
55.5	51
25	48.1
5.4	47.2
19	40.3
30.6	37.4
15.1	36.8
3.6	21.7
28.4	35.7
15	32
2.2	40.4
14.2	12.8
44.2	5.6
25.7	44.3
11.2	52.9
46.8	38
36.9	2.6
54.1	44.6
10.2	45.5
2.5	29.1
13.8	18.7
43.5	7
13.8	43.8
39.7	28.3
6.4	36.9
4.8	51.6

Using Excel

data -> data analysis -> t-Test: Two-Sample Assuming Unequal Variances

t-Test: Two-Sample Assuming Unequal Variances
	North	South
Mean	23.7	34.53333333
Variance	306.2551724	203.2995402
Observations	30	30
Hypothesized Mean Difference	0
df	56
t Stat	-2.6286
P(T<=t) one-tail	0.0055
t Critical one-tail	1.6725
P(T<=t) two-tail	0.0110
t Critical two-tail	2.0032

p-value = 0.011

p-value < alpha

hence we reject the null hypothesis

we conclude that means are significantly different