Stats 101 basic hypothesis testing questions 
The annual profit for your organisation last year was £1203,
per employee. The average for the sector was £1228 per employee.
You need to know if there is evidence that your organisation is not
as profitable, on average, as your competitors. The standard
deviation for the sector is £104 per employee.

Questions:

*

*State $H_0$ and $H_1$ for the test to check
Assuming that annual per employee profit follows a Normal distribution, the resulting P-value for the test is, P= 0.405 (3 d.p.):


*Based entirely on this P-value, what would you conclude from the test?


*What is the probability of getting a profit per employee  of £1203, or less, when there is no difference between that for your  company and the industry average?


*If your annual per employee profit was such that the test had resulted in a P-value given by P=0.032 and you were testing at  the α=0.01 significance level, what would you conclude and why?


*If you chose to reject $H_0$ but $H_0$ was actually true, would you be making a Type I or Type II error?


*What assumptions have you made about the annual per employee profit in this test?
 A: This is a very basic homework question testing the basic concepts of hypothesis testing from a introductory statistics course text.  As it is clearly homework I will sketch how to answer the questions.


*

*The null hypothesis is that your company's profits have the same value as the average of the other company's.  This tests whether or not a random observation from your company's distribution of profits can reasonably be considered to come from the distribution of profits for the competitors (when the competitors' distribution is assumed to be normal with mean 1228 and standard deviation 104.  What should the alternative be, one-sided or two?

*Since the p-value is high you can't reject the null hypothesis.  How would you state this in a conclusion?

*Form the z statistic (1203-1228)/104.  Look at the table of the statndard normal distribution and determine the probability that the standard normal is less than or equal to the z value that you computed.

*P is greater than the significance level 0.01, so you cannot reject.

*Falsely rejecting the null hypothesis is called a Type I error.

*Since you compare to a standard normal by subtracting the mean and dividing by the standard deviation of a normal distribution for the competitors what does the null hypothesis say about the distribution for your profits?
