### E | Solution Sheets

#### Hypothesis Testing With One Sample

Class Time: __________________________

*H*: ________{0}*H*: ________{a}- In words, clearly state what your random variable $\overline{X}$ or ${P}^{\prime}$ represents.
- State the distribution to use for the test.
- What is the test statistic?
- What is the
*p*-value? In one or two*complete sentences*, explain what the*p*-value means for this problem. - 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. - Indicate the correct decision (
*reject*or*do not reject*the null hypothesis), the reason for it and write appropriate conclusions using*complete sentences."*- Alpha: _______
- Decision: _______
- Reason for decision: _______
- Conclusion: _______

- Construct a 95 percent confidence interval for the true mean or proportion. 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: __________________________

*H*: ________{0}*H*: ________{a}- 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. - State the distribution to use for the test.
- What is the test statistic?
- What is the
*p*-value? In one to two*complete sentences,*explain what the*p*-value means for this problem. - 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. - Indicate the correct decision (
*reject*or*do not reject*the null hypothesis), and write appropriate conclusions using*complete sentences.*- Alpha: _______
- Decision: _______
- Reason for decision: _______
- Conclusion: _______

- In
*complete sentences,*explain how you determined which distribution to use.

#### The Chi-Square Distribution

Class Time: __________________________

*H*: ________{0}*H*: ________{a}- What are the degrees of freedom?
- State the distribution to use for the test.
- What is the test statistic?
- What is the
*p*-value? In one to two*complete sentences,*explain what the*p*-value means for this problem. - 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. - Indicate the correct decision (
*reject*or*do not reject*the null hypothesis) and write appropriate conclusions, using*complete sentences.*- Alpha: _______
- Decision: _______
- Reason for decision: _______
- Conclusion: _______

#### F Distribution and One-Way ANOVA

Class Time: __________________________

*H*: ________{0}*H*: ________{a}*df*(*n*) = ______*df*(*d*) = _______- State the distribution to use for the test.
- What is the test statistic?
- What is the
*p*-value? - 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. - Indicate the correct decision (
*reject*or*do not reject*the null hypothesis) and write appropriate conclusions, using*complete sentences*.- Alpha: _______
- Decision: _______
- Reason for decision: _______
- Conclusion: _______