## Tuesday, November 16, 2010

### Worked hypothesis test example

Here is an example of a typical Stephen P exam question with worked solution

15. You find that you get to love stats so much you want to take more courses! To pay the tuition fees, you get a job in a restaurant as a chef. The boss says that he always budgets for 120gm of smoked salmon in the smoked salmon omelette dish, but you suspect him of lying. You secretly measure the amounts over 42 samples. You find that the mean amount is 117gm with a sample standard deviation of 15gm. This is important: if the boss is lying you could blackmail him and get rich! (8)

a. Write the hypotheses

b. Test at 95%

c. Report your results

d. What are your conclusions?

Solutions....

a.

b. This is a two-tailed test. n > 30 so we could make use of the central limit theorem and use the normal distribution. But for myself I prefer to use the t distribution. So in Excel that’s =tdist(1.296,41,2)

giving you a p value of 0.202

c. We were asked to test at 95%, giving an alpha of 0.05. The p value that we calculated is larger than alpha (0.202 > 0.05) so following the rejection rule we fail to reject Ho.

d. Unfortunately (!) the boss is not lying so can’t blackmail him!