Solution Sheets, Front matter | Statistics

Learning objectives

Hypothesis Testing With One Sample

Class Time: __________________________
Name: _____________________________________

H₀: _______
H_a: _______
In words, clearly state what your random variable $\bar{X}$ or $P^{'}$ 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.

View original figure (external; image not reproduced in this text edition)

Original figure description: This is the frequency curve of a normal distribution with blank horizontal and vertical axes.
Indicate the correct decision (reject or do not reject the null hypothesis), the reason for it and write appropriate conclusions using complete sentences."
1. Alpha: _______
2. Decision: _______
3. Reason for decision: _______
4. 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.

View original figure (external; image not reproduced in this text edition)

Original figure description: This is the frequency curve of a normal distribution with blank horizontal and vertical axes.

Hypothesis Testing With Two Samples

Class Time: __________________________
Name: _____________________________________

H₀: _______
H_a: _______
In words, clearly state what your random variable ${\bar{X}}_{1} - {\bar{X}}_{2}$ , ${P^{'}}_{1} - {P^{'}}_{2}$ or ${\bar{X}}_{d}$ 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.
View original figure (external; image not reproduced in this text edition)
Original figure description: This is the frequency curve of a normal distribution with blank horizontal and vertical axes.
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: _______
In complete sentences, explain how you determined which distribution to use.

The Chi-Square Distribution

Class Time: __________________________
Name: ____________________________________

H₀: _______
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.
View original figure (external; image not reproduced in this text edition)

Original figure description: This is a right-skewed frequency curve with blank horizontal and vertical axes.
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: ____________________________________

H₀: _______
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.

View original figure (external; image not reproduced in this text edition)
Original figure description: This is an unlabeled number line.
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: _______

Attribution. Statistics, OpenStax, Rice University, and the contributing authors credited in the book. Licensed under Creative Commons Attribution 4.0 International. Source revision 7dea80ae28 of openstax/osbooks-statistics (2026-04-23). CC BY 4.0. Original source ↗. Text edition of a pinned CC BY 4.0 source revision of the OpenStax book, converted from CNXML by the EvidenceHelix importer. Original prose, learning objectives, tables, exercises, glossary and captions are preserved; images are not copied (figures link to the original source and keep their credits). No new content was added. Later revisions of this book can carry different licence terms and are not used.