solution

At Rachel’s 11th birthday party, 8 girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a 2-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.

Hypothesis Testing with Two Samples

1. H₀ : _______
2. H_a : _______
3. In words, clearly state what your random variable represents.
4. State the distribution to use for the test.
5. What is the test statistic?
6. What is the p-value? In one to two complete sentences, explain what the p-value means for this problem.
7. Use the previous information to sketch a picture of this situation. CLEARLY label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

Figure E3

1. Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.
   1. Alpha: _______
   2. Decision: _______
   3. Reason for decision: _______
   4. Conclusion: _______
2. In complete sentences, explain how you determined which distribution to use.