# help with Hypothesis testing question

#### artikiller

In a British study, 12 healthy college students deprived of one night’s sleep, received an array of tests intended to measure thinking time, fluency, flexibility and originality of thought. The overall test scores of the sleep-deprived students were compared to the average score expected from students who received their accustomed sleep (​
Sleep, Jan 1989). Suppose the overall scores of the 12 sleep-deprived students had a mean of 63 and a standard deviation of 17. (Lower scores are associated with a decreased ability to think creatively).

a)Test the hypothesis that the true mean score of sleep-deprived subjects is less than 80, the mean score of subjects who received sleep prior to taking the test.Use α = 0.05

and what function do I use in Excel to find the
P-value for this test.

Also what assumption is required for the hypothesis test of part a) to be valid?

#### matheagle

MHF Hall of Honor
what does excel have to do with anything?
This is simple enough.
Loading into a program most likely means you won't understand what you're doing.

$$\displaystyle H_0:\mu=80$$ vs. $$\displaystyle H_a:\mu< 80$$

where $$\displaystyle \mu$$ is the true mean score of sleep-deprived subjects.

The test statistic is a t with 11 degrees of freedom, it's value is

$$\displaystyle t^*_{11}={\overline X-\mu_0\over s/\sqrt{n}} ={63-80\over 17/\sqrt{12}}$$

which you can look up online http://www.danielsoper.com/statcalc/calc08.aspx
BUT with alpha equal to .05 you can obtain your rejection region and make a decidion based on this test stat.

The p-value is $$\displaystyle P(t_{11}<t^*_{11})$$

Assumptions are: all 12 are independent and normal rvs coming from the same distribution.