# Math Help - Determining a null and alternative hypothesis

1. ## Determining a null and alternative hypothesis

For a sample of 20 organizations, the mean score is 5.5 with a standard deviation of 2.8. You want to use this sample to test whether or not the organizations on average have an effectiveness score greater than 5.0.

(if you have time): Do the results of your sample permit you to accept the alternative hypothesis (use the appropriate value for a 95% confidence interval)

2. Originally Posted by endlesst0m

For a sample of 20 organizations, the mean score is 5.5 with a standard deviation of 2.8. You want to use this sample to test whether or not the organizations on average have an effectiveness score greater than 5.0.

H0: average effectiveness score is greater than 5.0

H1: average effectiveness score is less than 5.0

3. It's not clear what the hypotheses are.

I can see that this is a t test with 19 degrees of freedom.

I would go with...

$H_0:\mu=5$ vs $H_a:\mu >5$

and the Test Stat is

${\bar X-\mu_0\over s/\sqrt{n}} = {5.5-5\over 2.8/\sqrt{20}}$

The Rejection Region is $(t_{19,\alpha }, \infty)$

4. I'm not sure if that's the answer I'm looking for (for that last question). I don't know what a test stat is, or the degrees of freedom. This is just asking me if "the results of the sample permit me to accept the alternative hypothesis at the 95% confidence interval.