Question

*** Please answer all questions, not some. This entire discussion does count as one question w/ parts.

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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.  
   This is #3 completed:

   Contingency table results:

   
   Rows: Gender
   Columns: None

   Cell format

   Count
   (Expected count)

   	Alcohol Yes	Alcohol No	Total
   Male	77 (73.45)	404 (407.55)	481
   Female	16 (19.55)	112 (108.45)	128
   Total	93	516	609

   Chi-Square test:

   Statistic	DF	Value	P-value
   Chi-square	1	0.96169443	0.3268

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?

Answer 1

1.