Question

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                       50         28

   Female                   29         47


A. What is the calculated chi-squared value?

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

Answer 1

A. Chi-square test statistics

The formula of chi-square test statistics is,

where O - observed frequencies that are given.

E - Expected frequencies

The formula of expected frequencies is

There are two rows and two columns.

First row total = 78, second row total = 76

First column total = 79, second column total = 75 and overall total = 154

Expected value for 50 is

The expected value for 28 is,

Expected value for 29 is,

Expected value for 47 is,

The table for calculation of test statistics is,

O	E	(O - E)2
50	40.01299	99.74043	2.492701
28	37.98701	99.74043	2.625645
29	38.98701	99.74043	2.558299
47	37.01299	99.74043	2.694741
Total			10.37139

B. Critical value = 3.84

Decision rule: If critical value > test statistics then fail to reject the null hypothesis otherwise reject the null hypothesis.

Critical value (3.84) is less than test statistics (10.37) so reject the null hypothesis.

Conclusion: There is a significant relationship between gender and alcohol-related arrests.