Question

4. [7 marks] Consider two independent populations. We took two SRS of sizes 10 from each population and x1 = 525.751, $ı = 107.121, x2 = 373.269 and s2 = 67.498 Is there enough evidence to reject the null hypothesis in the following test? (a = 1%) HO: H1 - H2 = 0 H:H - H2> 0 1

Answer 1

Solution:

The test statistic t is given by

t =

T1 T2 + ) 111 112

where   $url=https://latex.codecogs.com/gif.latex?s_%7Bp%7D%5E%7B2%7D&t=1596159474&ymreqid=f4764063-0d40-e2b0-1cde-f0004d012f00&sig=QCHJiyuFG2Uuq3gHNKpgmg--~D$ denotes the pooled variance.

Therefore ,

t =

11 - 12 (nı-1)s+(12-1)s ni+n2-2 om + 11 n2

=

525.751 - 373.269 (10-10107.1212 + (10-1067.498211 10-10-2 10 (+

= 3.808

Test statistic t = 3.808

d.f. = n₁ + n₂ - 2 = 10 + 10 - 2 = 18

> sign in Ha indicates that " One tailed right sided test"

$\alpha$ = 1% = 0.01

For right tailed test , critical value is

tads +0.01.18 = 2.552

Test statistic t = 3.808 > 2.552

So , Reject H₀

Yes , there is enough evidence to reject the null hypothesis