Random sampling-level of significance

Question

Random samples of house selling prices are obtained from the north and south regions of a country. The results are summarized below:

                     North        South

sample size:          50           80

mean house price:     150000       160000

standard deviation:   20000       25000

At the $5\%$ level of significance, test the claim that the house selling prices are the same in the regions.

Answer 1

You can apply an unpaired t-test.

$H_0: \mu_x=\mu_y$

$H_1: \mu_x\neq \mu_y$

The test value is

$\large{t=\sqrt{\frac{nm}{n+m}}\cdot \frac{\overline x -\overline y}{s}}$

with $s^2=\frac{(n-1)\cdot s_x^2+(m-1)\cdot s_y^2}{n+m-2}$

If $\large{|t|>t_{(1-\frac{\alpha}{2},n+m-2)}}$, then you reject the Null-Hypothesis.

$\alpha=0.05$

The value for $t_{(0.975,128)}$ can be looked up here (one tail).

The degree of freedom is $df=50+80-2=128$