The means of two samples of sizes 1000 and 2000 respectively are 67.50 and 68.0 inches. Can the samples b regarded as drawn from the same population of S. D. 2.5 inches?

7.8kviews

written 8.7 years ago by

teamques10 ★ 69k

Given -

$\overline{x_1}=67.5\ ,\ \overline{x_2}=68 n{}_{1}=1000 n{}_{2}=2000$

Step 1 :-

Null Hypothesis (H ${}_{0}$ ): $\mu$ ${}_{1}$ = $\mu$ ${}_{2}$ Alternative Hypothesis (H ${}_{\mathrm{\infty}}$ )= $\mu$ ${}_{1}$ $\mathrm{\neq}$ $\mu$ ${}_{2}$ Step 2 :- Test Statistic:-

$\overline{x_1}-\overline{x_2}=67.5-68.0=-0.5$

Since S.D. of the population is known

$S.E. S=\sqrt{\frac{{\sigma }^2_1}{n_1}+\frac{{\sigma }^2_2}{n_2}}$

$=\sigma \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$

$=\sqrt{\frac{1}{1000}+\frac{1}{2000}}$

$=0.097$

$\mathrm{\therefore } z=\frac{\overline{x_1}-\overline{x_2}}{s}=\frac{-0.5}{0.097}=-5.15$

$\mathrm{\therefore } |z| = 5.15$

Step 3 :- Level of significance $\mathrm{\propto }$ =0.27%

Step 4 :-

Critical Value

The value of Z ${}_{\mathrm{\propto }}$ at 0.27% level of significance from table is 3

Step 5 :- Decision

Since the computed value of |z|=5.15 is greater than critical value z ${}_{\mathrm{\propto }}$ =3 the hypothesis is rejected.

$\mathrm{\therefore }$ The sample can not be regarded as drawn from same population.

ADD COMMENT EDIT