A physiologist believes he has discovered a new steroid hormone that can control the blood glucose in mammals. In an experiment he injects laboratory rats with a small amount of this steroid hormone and, after a suitable waiting period measures the blood glucose level of the rats. In his twelve experimental rats he obtains the following levels of blood glucose {35,36,37,33,34,35,33,35,37,36,34,3 5}. From previous studies of thousands of normal, un-manipulated rats he knows that the mean (mu) blood glucose level in this species of rat (his laboratory population) is 31 and that the standard deviation is 4.12. Evaluate the hypothesis that this new steroid hormone affects blood glucose levels. Use an alpha-level of 0.01 for this analysis. Required:
a. What is the appropriate test?
b. State the null hypothesis.
c. State the alternative hypothesis.
d. Find the critical value.
e. Calculate the obtained statistic.