0.1 Appendix a: solution sheets

Hypothesis testing with one sample

Class Time: __________________________
Name: _____________________________________

1. H ₀ : _______
2. H _a : _______
3. In words, CLEARLY state what your random variable $\overline{X}$ or $P^{\prime }$ represents.
4. State the distribution to use for the test.
5. What is the test statistic?
6. What is the p -value? In one or 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.

   

8. 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: _______
9. Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval.

   

Hypothesis testing with two samples

Class Time: __________________________
Name: _____________________________________

1. H ₀ : _______
2. H _a : _______
3. In words, clearly state what your random variable ${\overline{X}}_1-{\overline{X}}_2$ , ${P^{\prime }}_1-{P^{\prime }}_2$ or ${\overline{X}}_d$ 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.

   

8. 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: _______
9. In complete sentences, explain how you determined which distribution to use.

The chi-square distribution

Class Time: __________________________
Name: ____________________________________

1. H ₀ : _______
2. H _a : _______
3. What are the degrees of freedom?
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.

   

8. Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write appropriate conclusions, using complete sentences.
   1. Alpha: _______
   2. Decision: _______
   3. Reason for decision: _______
   4. Conclusion: _______

F distribution and one-way anova

Class Time: __________________________
Name: ____________________________________

1. H ₀ : _______
2. H _a : _______
3. df ( n ) = ______ df ( d ) = _______
4. State the distribution to use for the test.
5. What is the test statistic?
6. What is the p -value?
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.

   

8. Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write appropriate conclusions, using complete sentences .
   1. Alpha: _______
   2. Decision: _______
   3. Reason for decision: _______
   4. Conclusion: _______