Question

In a test given to two groups of students, the marks obtained are as follows:

First Group 18, 20, 36, 50, 49, 36, 34, 49, 41.
Second Group 29, 28, 26, 35, 30, 44, 46.

Examine the significance of the difference between the arithmetic mean of the marks secured by the students of the above two groups.​

Answer 1

Answer:

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Answer 2

Given :

First Group       : 18, 20, 36, 50, 49, 36, 34, 49, 41

Second Group  : 29, 28, 26, 35, 30, 44, 46

To find :

Examine the significance of the difference between the arithmetic mean of the marks secured by the students of the above two groups.​

Solution :

$x' = \frac{\sum x_i }{n_1 } = \frac{333}{9} = 37\\\\s_1^{2} = \frac{\sum (x_i-x')^{2} }{n_1-1 } = \frac{1134 }{9-1} = 141.75$

$y' = \frac{\sum y_i }{n_2 } = \frac{238}{7} = 34\\\\s_2^{2} = \frac{\sum (y_i-y')^{2} }{n_2-1 } = \frac{386 }{7-1} = 64.33$

Null Hypothesis : H₀ : μ₁ = μ₂

Alternative Hypothesis : H₁ : μ₁ ≠ μ₂

$t = \frac{x_1'-x_2' }{\sqrt{\frac{s_1^{2} }{n_1} } + \frac{s_2^{2} }{n_2} }$

|t| = 0.57

The critical value fort t for a two tailed test at 5% level of significance with

9 + 7 - 2 = 14     (n₁ + n₂ - 2)

Degree of freedom = 1.76

Calculated value = 0.57

Tabulated value = 1.76

|Calculated value| < Tabulated value , then accept H₀

|0.57| < 1.76 , accept H₀

Conclusion : There is no significant difference between the mean marks secured by the two groups