4-3-10-variation-t-test-worked-example

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Variation: t-test worked example

The t test method can be used to determine whether the means of two data sets are significantly different

The ear lengths of two populations of rabbits were measured.

Ear lengths of population A (mm):

62, 60, 59, 61, 60, 58, 59, 60, 57, 56, 59, 58, 60, 59, 57

Ear lengths of population B (mm):

58, 59, 57, 59, 59, 57, 55, 60, 57, 58, 59, 58, 57, 58, 59

Use the t-test to determine whether there is a significant difference in ear length between the two populations.

Null hypothesis: There is no significant difference between the ear lengths of the rabbits in populations A and B
Sample sizes:
- Population A: n₁ = 15
- Population B: n₂ = 15

Step 1: calculate the mean for each data set:

Mean for population A x̅₁ = 885 ÷ 15 = 59 mm

Mean for population B x̅₂= 870 ÷ 15 = 58 mm

Step 2: calculate the standard deviation (s) for each data set

Population A		Population B
Difference between value and mean (x – x̄)	Difference between value and mean squared (x – x̄)²	Difference between value and mean (x – x̄)	Difference between value and mean squared (x – x̄)²
62 – 59 = 3	9	58 – 58 = 0	0
60 – 59 = 1	1	59 – 58 = 1	1
59 – 59 = 0	0	57 – 58 = -1	1
61 – 59 = 2	4	59 – 58 = 1	1
60 – 59 = 1	1	59 – 58 = 1	1
58 – 59 = -1	1	57 – 58 = -1	1
59 – 59 = 0	0	55 – 58 = -3	9
60 – 59 = 1	1	60 – 58 = 2	4
57 – 59 = -2	4	57 – 58 = -1	1
56 – 59 = -3	9	58 – 58 = 0	0
59 – 59 = 0	0	59 – 58 = 1	1
58 – 59 = -1	1	58 – 58 = 0	0
60 – 59 = 1	1	57 – 58 = -1	1
59 – 59 = 0	0	58 – 58 = 0	0
57 – 59 = -2	4	59 – 58 = 1	1
Total ∑(x – x̄)²	36	Total ∑(x – x̄)²	22

Calculate $square root of fraction numerator sum for blank of open parentheses straight x minus straight x with bar on top close parentheses squared over denominator straight n minus 1 end fraction end root$

Population A (n₁ = 15)