Solution Sheets

Hypothesis Testing with One Sample

Class Time: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_* * *

Name: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

1. H₀: \_\_\_\_\_\_\_
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. H₀: \_\_\_\_\_\_\_
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. H₀: \_\_\_\_\_\_\_
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. H₀: \_\_\_\_\_\_\_
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: \_\_\_\_\_\_\_

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