Registrar's Office conducted a study of independence between two binary variables, (X,Y), Variable X indicates individual performance (High or Low) and Y characterizes a student's status (Graduate or 600 respondents has shown summaries as follows. Observed Frequencies Undergraduate). A group of n = Undergraduate Graduate Row Sum High 311 139 450 Low 89 61 150 Column Sum 400 200 600 Expected Counts Undergraduate Graduate Row Sum High 450 Low 150 Column Sum 400 200 600 Test independence of (X, Y) at the significance level a = 0.05

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Registrar's Office conducted a study of independence between two binary variables, (X, Y), Variable
X indicates individual performance (High or Low) and Y characterizes a student's status (Graduate or
Undergraduate). A group of n = 600 respondents has shown summaries as follows.
Observed Frequencies
Undergraduate Graduate
Row Sum
High
311
139
450
Low
89
61
150
Column Sum
400
200
600
Expected Counts
Undergraduate Graduate
Row Sum
High
450
Low
150
Column Sum
400
200
600
Test independence of (X, Y) at the significance level a = 0.05
• Find ESTIMATED EXPECTED COUNTS under the null hypothesis of homogeneity / inde-
pendence between gender and satisfaction and place them into the table provided above.
• Evaluate the TEST STATISTIC for this study
• Specify CRITICAL VALUE (or VALUES) required for hypothesis testing procedure.
• Formulate REJECTION RULE and then state your decision about independence.
Next page is reserved for DETAILED solution.
Transcribed Image Text:Registrar's Office conducted a study of independence between two binary variables, (X, Y), Variable X indicates individual performance (High or Low) and Y characterizes a student's status (Graduate or Undergraduate). A group of n = 600 respondents has shown summaries as follows. Observed Frequencies Undergraduate Graduate Row Sum High 311 139 450 Low 89 61 150 Column Sum 400 200 600 Expected Counts Undergraduate Graduate Row Sum High 450 Low 150 Column Sum 400 200 600 Test independence of (X, Y) at the significance level a = 0.05 • Find ESTIMATED EXPECTED COUNTS under the null hypothesis of homogeneity / inde- pendence between gender and satisfaction and place them into the table provided above. • Evaluate the TEST STATISTIC for this study • Specify CRITICAL VALUE (or VALUES) required for hypothesis testing procedure. • Formulate REJECTION RULE and then state your decision about independence. Next page is reserved for DETAILED solution.
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