Comparison of student's performance involved the total of n = 600 respondents. Two groups selected were: Undergraduate and Graduate. Individual performance was measured in a binary scale (Pass or Fail). The summaries are presented below. Group Size Pass Proportion Graduate n1 = 200 X = 139 (p)1 = 139/200 = 0.6950 Undergraduate n2 = 400 X2= 311 (f)2 = 311/400 = 0.7775 Pooled n = nj + n2 = 600 X = X1+ X2 = 450 p= 450/600 = 0.75 At the significance level, a = 0.05, do you have sufficient evidence that population proportions DIFFER? • Evaluate the test statistic Specify critical value (or values) needed for this procedure. • State the Rejection Rule • Formulate your decision Solution

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Comparison of student's performance involved the total of n = 600 respondents. Two groups selected were:
Undergraduate and Graduate. Individual performance was measured in a binary scale (Pass or Fail).
The summaries are presented below.
Group
Size
Pass
Proportion
Graduate
ni = 200
X1 = 139
(p)1 = 139/200 = 0.6950
Undergraduate
n2 = 400
X2 = 311
(p)2 = 311/400 = 0.7775
Pooled
n = nị + n2 = 600
X = X1+ X2 = 450
p= 450/600 = 0.75
At the significance level, a = 0.05, do you have sufficient evidence that population proportions DIFFER?
• Evaluate the test statistic
• Specify critical value (or values) needed for this procedure.
• State the Rejection Rule
• Formulate your decision
Solution
Transcribed Image Text:Comparison of student's performance involved the total of n = 600 respondents. Two groups selected were: Undergraduate and Graduate. Individual performance was measured in a binary scale (Pass or Fail). The summaries are presented below. Group Size Pass Proportion Graduate ni = 200 X1 = 139 (p)1 = 139/200 = 0.6950 Undergraduate n2 = 400 X2 = 311 (p)2 = 311/400 = 0.7775 Pooled n = nị + n2 = 600 X = X1+ X2 = 450 p= 450/600 = 0.75 At the significance level, a = 0.05, do you have sufficient evidence that population proportions DIFFER? • Evaluate the test statistic • Specify critical value (or values) needed for this procedure. • State the Rejection Rule • Formulate your decision Solution
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