Seven Steps for Doing  2 1) State the hypothesis 2) Create data table 3) Find  2 critical 4) Calculate the expected frequencies 5) Calculate  2 6) Decision 7) Put answer into words

Example With whom do you find it easiest to make friends? Subjects were either male and female. Possible responses were: “opposite sex”, “same sex”, or “no difference” Is there a significant (.05) relationship between the gender of the subject and their response?

Results

Step 1: State the Hypothesis H 1: There is a relationship between gender and with whom a person finds it easiest to make friends H 0 :Gender and with whom a person finds it easiest to make friends are independent of each other

Step 2: Create the Data Table

Add “total” columns and rows

Step 3: Find  2 critical df = (R - 1)(C - 1)

Step 3: Find  2 critical df = (R - 1)(C - 1) df = (2 - 1)(3 - 1) = 2  =.05  2 critical = 5.99

Step 4: Calculate the Expected Frequencies Two steps: 4.1) Calculate values 4.2) Put values in your data table

Step 4: Calculate the Expected Frequencies E = (73 * 137) /205 = 48.79

Step 4: Calculate the Expected Frequencies E = (73 * 68) /205 = 24.21

Step 4: Calculate the Expected Frequencies E = (29 * 137) /205 = 19.38

Step 4: Calculate the Expected Frequencies

Step 5: Calculate  2 O = observed frequency E = expected frequency

22

22

22

22

22 8.5

Step 6: Decision Thus, if  2 > than  2 critical –Reject H 0, and accept H 1 If  2 < or = to  2 critical –Fail to reject H 0

Step 6: Decision Thus, if  2 > than  2 criticalThus, if  2 > than  2 critical –Reject H 0, and accept H 1 If  2 < or = to  2 critical –Fail to reject H 0  2 = 8.5  2 crit = 5.99

Step 7: Put answer into words H 1: There is a relationship between gender and with whom a person finds it easiest to make friends A persons gender is significantly (.05) related with whom it is easiest to make friends.

Practice Is there a significant (  =.01) relationship between opinions about the death penalty and opinions about the legalization of marijuana? 933 Subjects responded yes or no to: “Do you favor the death penalty for persons convicted of murder?” “Do you think the use of marijuana should be made legal?”

Results Marijuana ? Death Penalty ?

Step 1: State the Hypothesis H 1: There is a relationship between opinions about the death penalty and the legalization of marijuana H 0 :Opinions about the death penalty and the legalization of marijuana are independent of each other

Step 2: Create the Data Table Marijuana ? Death Penalty ?

Step 3: Find  2 critical df = (R - 1)(C - 1) df = (2 - 1)(2 - 1) = 1  =.01  2 critical = 6.64

Step 4: Calculate the Expected Frequencies Marijuana ? Death Penalty ?

Step 5: Calculate  2

Step 6: Decision Thus, if  2 > than  2 critical –Reject H 0, and accept H 1 If  2 < or = to  2 critical –Fail to reject H 0

Step 6: Decision Thus, if  2 > than  2 critical –Reject H 0, and accept H 1 If  2 < or = to  2 criticalIf  2 < or = to  2 critical –Fail to reject H 0  2 = 3.91  2 crit = 6.64

Step 7: Put answer into words H 0 :Opinions about the death penalty and the legalization of marijuana are independent of each other A persons opinion about the death penalty is not significantly (.01) related with their opinion about the legalization of marijuana

Practice In a large corporation, the mean salary for all males with 3 to 5 years of experience was $28,000. Salaries (expressed in thousands) for a random sample of 10 women also having 3 to 5 years of experiences were: 24, 27, 31, 21, 19, 26, 30, 22,15, 36 Is there evidence of different salary levels (alpha =.05) for males and females?

Practice One-sample t-test t = Do not reject Ho. There is not evidence of a real salary difference between men and women