MATH 160 Cuyamaca College W25 Chi Square Test Discussion

I’m working on a statistics discussion question and need a sample draft to help me understand better.

Progress Check

Use this activity to assess whether you and your peers can:

• Conduct a chi-square test of independence. Interpret the conclusion in context.

Learn by Doing

In this activity we practice the Chi-square Test for Independence in its entirety using StatCrunch.

Some features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.

Use the rubric at the bottom of this page as a guide for completing this assignment.

A list of StatCrunch directions is provided after the Prompt section below.

Directions

Submit your work:

• Carefully read all sections below (beginning with the Context section and ending with the Prompt section).
• Commit a good-faith effort to address all items in the Prompt section below. Please be sure to number your responses.
• If directed to do so, embed all required StatCrunch output in your initial submission. Please do not submit StatCrunch output as an attachment.

Complete your assigned peer reviews:

• After you submit your initial good-faith attempt, continue to the ANSWER(S) page and review your instructor’s response. But please do not submit your corrected work yet.
• Within three days after the due date, return to this assignment and complete your assigned peer reviews (directions (Links to an external site.)).

Submit your corrected work:

• We all learn from mistakes (our own and our classmates’ mistakes). So please do not immediately correct your own mistakes. If possible, wait until you receive feedback from at least one of your peers.
• If necessary, correct your work and resubmit the entire assignment – including any required StatCrunch output. Your instructor will only review and grade your most recent submission, so please do not refer to a previous submission.

Context – A Real Court Case

In the early 1970s, a young man challenged an Oklahoma state law that prohibited the sale of 3.2% beer to males under age 21 but allowed its sale to females in the same age group. The case (Craig v. Boren, 429 U.S. 190, 1976) was ultimately heard by the U.S. Supreme Court. The state of Oklahoma argued that the law improved traffic safety. One of the three main pieces of data presented to the court was the result of a “random roadside survey.” This survey gathered information on gender and whether or not the driver had been drinking alcohol in the previous 2 hours. A total of 619 drivers under 21 years of age were included in the survey.

Prompt

1. A test of independence may be appropriate if we are examining the relationship between two categorical variables in one population. For this situation what is the population? What is the explanatory variable? What is the response variable?
2. What are the hypotheses for the Test of Independence? State hypotheses with reference to the context of the scenario.
3. The spreadsheet of the data looked like this:
   

   Roadside survey data

   Driver	Gender	Alcohol in last two hours?
   Driver 1	M	Yes
   Driver 2	F	No
   Driver 3	F	Yes
   . . .	. . .	. . .
   Driver 619	M	No

   We will not use the raw data. Instead we will use the summarized data shown in the table below.

   Roadside survey summary

   Drank alcohol in last 2 hours?	Yes	No	Totals
   Male	77	404	481
   Female	16	122	138
   Totals	93	526	619

   Use StatCrunch to find expected counts, the Chi-square test statistic and the P-value. (directions)
   Copy and paste your StatCrunch table into your post.

4. How many males in the sample are expected to answer yes to question about alcohol consumption in the last two hours? Show how to calculate this expected count and explain what it means relative to the hypotheses.
5. Explain how we know that this data meets the conditions for use of a chi-square distribution.
6. State a conclusion at a 5% level of significance. Do you think that the data supports the Oklahoma law that forbids sale of 3.2% beer to males and permits it to females?

List of StatCrunch Directions

Each link will open in a new window. To return to this discussion, either close the new tab or select the tab for this discussion.

• Purchase StatCrunch (You only need to do this once.)
• Open StatCrunch
• Download Excel Data File
• Upload Excel Data File to StatCrunch
• Download StatCrunch Output Window (no screenshots; please use these directions)
• Upload Files into Your Stat-Class Folder in Canvas
• Embed Pictures in a Discussion Post (no attachments; please use these directions)
• Chi-square Test for Independence (Summarized Data)

Rubric

Peer Reviewed Assignment w/ StatCrunch

Peer Reviewed Assignment w/ StatCrunch

Criteria	Ratings	Pts
This criterion is linked to a Learning OutcomeAddressing the Prompt	6 pts Full Marks All parts of the Prompt are addressed. Answers are correct. Statistical vocabulary is used appropriately. Writing is clear and thought process is easy to follow. 4 pts Partial Credit Some parts of the prompt are not addressed, are incorrect, or are unclear. 0 pts No Marks The prompt is not addressed.	6 pts
This criterion is linked to a Learning OutcomeStatCrunch Data	2 pts Full Marks Appropriate StatCrunch graphs and/or tables are provided as directed. 1 pts Partial Credit StatCrunch graphs and tables are inappropriate or missing important information. 0 pts No Marks No StatCrunch information is provided.	2 pts
This criterion is linked to a Learning OutcomeIndividual Penalty	0 pts No individual penalty -1 pts Individual penalty. Please see the instructor comments for more information.	0 pts
This criterion is linked to a Learning OutcomePeer Reviews	2 pts Full Marks You completed all assigned peer reviews (maximum of 2). For each peer review, the points you assigned in the rubric are appropriate. You included comments explaining the score you posted in the rubric. If you deducted points in the rubric, your comments explain what the author needs to do to earn a higher grade when the teacher grades the assignment. 1 pts Partial Credit Committed a good-faith effort to provide a high-quality peer review, but many necessary instructive comments are missing. 0 pts No Marks No peer review provided or the comments are not instructive.	2 pts
Total Points: 10