Question

The Independent-sample t-test

Is there any evidence that leadership style (as measured by the amount of controlling behavior) differs between principals in urban and rural areas in Oromia? Data are provided below:
Urban: 78.56 Roral: 69.60
s = 16.7 s = 19.31
n = 9 n = 10

Answer 1

Conditions

The Independent-sample t-test

Is there any evidence that leadership style (as measured by the amount of controlling behavior) differs between principals in urban and rural areas in Oromia? Data are provided below:

Urban: 78.56

Roral: 69.60

s = 16.7

s = 19.31

n = 9

n = 10

Solution

The t-stats for independent-sample t-test is:

$$t = \frac {\bar {X} _ {1} - \bar {X} _ {2}}{S _ {X _ {2} X _ {2}} \sqrt {\frac {1}{n _ {1}} + \frac {1}{n _ {2}}}},$$ $$S _ {X _ {1} X _ {2}} = \sqrt {\frac {1}{2} \left(S _ {X _ {1}} ^ {2} + S _ {X _ {2}} ^ {2}\right)}$$ $$S _ {X _ {1}} ^ {2} = \frac {\sum_ {i = 1} ^ {11} \left(X _ {1} - M _ {1}\right) ^ {2}}{n}$$ $$S _ {X _ {2}} ^ {2} = \frac {\sum_ {i = 1} ^ {11} \left(X _ {2} - M _ {2}\right) ^ {2}}{n}$$ $$t = \frac {8,96}{8,29} = 1,08$$

The degrees of freedom:

$$k = 22 - 2 = 20$$

The t-criterion value is 2.5668 (for $p = 0.95$).

As our t is lesser, than t-criterion value, so the null hypothesis is approved.

**Answer: YES**