Question

Refer to the hormone analysis discussed in Lecture 25. You will be analyzing the data from Experiment B as below:

"Fresh","Frozen"

1.97,1.88

4.1,4.11

3.02,2.99

8.31,8.28

2.69,2.62

3.16,3.16

2.73,2.72

2.46,2.47

3.6,3.6

5.35,5.35

6.03,6.05

3.2,3.16

2.91,2.89

4.57,4.53

2.75,2.73

1.91,1.87

4.95,4.95

5.23,5.22

3.39,3.37

We are interested in whether mean hormone concentration decreases if the sample is frozen before analyzing. You may assume that differences in concentration (fresh vs. frozen) within a single blood sample are normally distributed. a. Explain why the design of Experiment B is a matched pairs design. b. What are the null and alternative hypotheses? c. (1 mark) What is the test statistic? d. (1 mark) What is the distribution if the null hypothesis is true? e. What is the p-value? f. State your conclusions about this test in the language of the problem.  

Answer 1

a). The design of Experiment B is a matched pair design because the Sample Fresh and frozen are taken from a single blood sample.

b) Null and Alternative Hypotheses

where = differnce between Fresh and frozen

c).

For the score differences we have

Test Statistics

d). If the null hypothesis is true than the samples fresh and frozen have no differnece in concentraction. The mean hormone concentration remains same for fresh and frozen samples.

e). P- value = 0.0029

f). If the p > (signifiacnce level), then we do not reject null hypothesis, that will mean the fresh and frozen sample have no differnce in concentration.

But if p < , then we reject null hypothesis, that will mean the fresh sample have more concentration than frozen sample or frozen sample have less concentration than fresh sample.