# Math Help - Hypothesis Testing

1. ## Hypothesis Testing

Hi guys, I need some help with this one ( mainly "1" and "2" ):

A research check tails of 40 cats. these are the results:

average s.d n
Males 190 15 22

Famales 180 12 18

1. check the hypothesis that the tails of the males are longer, with significant level of 10%.

2. what is the significant of the result ? ( p value )

3. build a confidence interval of 90% to the mean difference

2. Originally Posted by weeg
average s.d n
males 190 15 22

famales 180 12 18

3. Build a confidence interval of 90% to the mean difference
$(\mu_1 - \mu_2) \pm t_{(.9,40-2)} \times \left( \sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2 }}\right)$

$(190 - 180) \pm t_{(.9,40-2)} \times \left( \sqrt{\frac{15^2}{22}+\frac{12^2}{18}}\right)$

3. You should be pooling the two sample variances if you're using 40-2 degrees of freedom.
That means you are assuming equal varainces.
Otherwise if you use the above standard deviation you need Satherwaithe's approximation for the degrees of freedom.
I would do a one sided test where Ha is the claim that the male's tail is longer on average.

4. My changes...

$\bar x_1 - \bar x_2 \pm t_{38,.05} s_p \sqrt{{1\over n_1}+{1\over n_2}}$