Means of two random samples of size 9 & 7 are 196.42 & 198.82 respectively. Sum of squares of deviation from means is 26.94 & 18.73. Can sample be considered to have been drawn from same population?

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written 8.7 years ago by

teamques10 ★ 69k

modified 3.0 years ago by

sagarkolekar ★ 11k

engineering mathematics

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written 8.7 years ago by

teamques10 ★ 69k

• modified 8.7 years ago

n ${}_{1}$ =9 \& n ${}_{2}$ =7( $\lt$ 30 , so it is small sample)

$\overline{x_1}=196.42\ ;\ \overline{x_2}=198.82\ ;\ \sum{{(x_{1i}-\overline{x_2})}^2=26.94\ ;\ {(x_{2i}-\overline{x_2})}^2=18.73}$

Step 1 :-

Null Hypothesis (H ${}_{0}$ ): $\mu$ ${}_{1}$ = $\mu$ ${}_{2}$ (i.e. Samples are drawn from the same population) Alternative Hypothesis (H ${}_{\mathrm{\infty}}$ )= $\mu$ ${}_{1}$ $\mathrm{\neq}$ $\mu$ ${}_{2}$ (i.e. Samples are not drawn from the same population) (Two tailed test) Step 2 :- LOS=5% (Two tailed test) …

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