Question

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 {35,36,37,33,34,35,33,35,37,36,34,35}. 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.

Answer 1

1.) One sample t test

2.) New steroid does not decrease blood glucose level in rats ; H0 : μ = 31

3.) New steroid does blood glucose level in rats ; H1 : μ ≠ 31

4.) 2.718

5.) 3.36

Explanation:

We only have one sample; hence, we use an independent sample t test.

Given the sample data :

X : 35,36,37,33,34,35,33,35,37,36,34,35

Using calculator;

Sample mean, Xbar = 35

Null hypothesis ;supports that the mean glucose level of species equals ; H0 : μ = 31

The alternative hypothesis ; H1 negates the null hypothesis and aligns with the sample mean ; 35 > 31 ;

H1 : μ > 31

The critical value can be obtained from the T-distribution table ;

α = 0.01 ; degree of freedom, df = n - 1 = 12 - 1 = 11

Tcritical value = 2.718

Tstatistic : (xbar - μ) ÷ (s/√n)

Tstatistic = (35 - 31) ÷ (4.12/√12)

Tstatistic = 3.36

Tstatistic is more extreme Than the critical value