Question

You hypothesize that average rectal tumor size is related to the ecology of the gut, and in particular the way the appendix works. As the appendix does strongly influence the bacterial fauna within a persons gut system, this makes sense. To start off your investigation, you do a pilot study comparing tumor masses in people with and without their appendix. You look at 14 people, 7 with and 7 without a tumor. The people are randomly sampled from the population of people with rectal cancer. You get the following data:

Person	Tumor Size (g)	With Appendix?	Person	Tumor Size	With Appendix?
1	420	Y	8	434	N
2	942	Y	9	601	N
3	688	Y	10	422	N
4	794	Y	11	553	N
5	659	Y	12	512	N
6	811	Y	13	499	N
7	845	Y	14	415	N

Conduct a t-test, and calculate the p-value, then answer the following questions.

1. a) What is the difference in means?

   b) What are the assumptions that go into using a t-test appropriately?

   c) Calculate the p-value using the appropriate degrees of freedom and the tables in the back of your book. What is it?

   d) What is your null hypothesis?

   e) Does your p value support your hypothesis, not support the null hypothesis, or both?

   f) What can you conclude from your investigation?

Answer 1

a) Difference in means = 246.1429

b) Assumptions -

1) simple random sample, that the data is collected from a representative.

2)Data, when plotted, results in a normal distribution, bell-shaped distribution curve.

3)Reasonably large sample size is used.

4) Homogeneity of variance.

c) p value = 0.003978 , degrees of freedom = 12

d) H1 : Means of two groups doesn't differ significantly.

e) p value <0.05 , which means that it fail to reject null hypothesis.

f) Conclusion - Average rectal tumor size is related to the ecology of the gut, and in particular the way the appendix works is not different . PL??