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W75A - Please answer in detail using EXCEL Function T-test of 2 means (Similar to presentation in class;...

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Basic Math

W75A - Please answer in detail using EXCELFunction

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

             (Wednesday class)

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

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

(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 & Explanation Solved by verified expert
4.0 Ratings (614 Votes)

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
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