Question

Q1. In a study of binge drinking among undergraduates at Ohio University, a researcher was interested in gender differences as related to binge drinking and to drinking-related arrests. She wanted to know two things: (a) Is there a significant relationship between gender and binge drinking (as defined by 5 or more drinks at one sitting), and (b) Is there a significant relationship between gender and drinking-related arrests? A random sample of males and females were asked about their experiences with binge drinking and with drinking-related arrests.

Use the numbers below for this question only!

                  Experience Alcohol-related Arrest?

  YES        NO

   Male                       279         254

   Female                   293         254


What would the expected value for the "male-no" cell be?

Q2. In a study of binge drinking among undergraduates at Ohio University, a researcher was interested in gender differences as related to binge drinking and to drinking-related arrests. She wanted to know two things: (a) Is there a significant relationship between gender and binge drinking (as defined by 5 or more drinks at one sitting), and (b) Is there a significant relationship between gender and drinking-related arrests? A random sample of males and females were asked about their experiences with binge drinking and with drinking-related arrests.

Use the numbers below for this question only!

                  Experience Alcohol-related Arrest?

  YES        NO

   Male                       202         287

   Female                   230         220


What would the expected value for the "female-yes" cell be?

Q3. In a study of binge drinking among undergraduates at Ohio University, a researcher was interested in gender differences as related to binge drinking and to drinking-related arrests. She wanted to know two things: (a) Is there a significant relationship between gender and binge drinking (as defined by 5 or more drinks at one sitting), and (b) Is there a significant relationship between gender and drinking-related arrests? A random sample of males and females were asked about their experiences with binge drinking and with drinking-related arrests. Test for a relationship in the following data:

Use the numbers below for this question only!

                  Experience Alcohol-related Arrest?

  YES        NO

   Male                       43         29

   Female                   28         39


What is the calculated chi-squared value?

Q4.

Using a critical value of 3.84, and based on the obtained chi-square value in Question 13, is there a significant relationship between gender and alcohol-related arrests?

Yes

No

Answer 1

1)

	yes	no	Total
male	279	254	533
female	293	254	547
total	572	508	1080

expected value for the "male-no" cell be =row total*column total/grand total=(533*508/1080)

=250.707

2)

expected value for the "female-yes" cell be =432*450/939 =207.029

3)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	yes	no	Total
	male	36.780	35.223	72.00302158
	female	34.223	32.777	67
	total	71.00302158	68	139.0030216
chi square    χ2	=(Oi-Ei)2/Ei	yes	no	Total
	male	1.052	1.099	2.1513
	female	1.132	1.181	2.3131
	total	2.1835	2.2810	4.464
test statistic X2 =		4.464

4)

yes, since test statistic is higher than critical value