University officials hope that changes they have made have improved the retention rate. In 2010, a sample of 1926 freshmen showed that 1400 returned as sophomores. In 2011, 1508 of 2011 freshmen sampled retumed as sophomores. Determine if there is sufficient evidence at the 0.05 level to say that the retention rate has improved. Ho: P1 = P2 H₁: P₁ P2 p = x₁+x2 = n₁+n₂ Z= P₁ = 1400 1926 1400+1505 1926+2011 =.73 2905 3937 Z= = .74 (P1-P2)-(P1-P2) √(1-P)(²+1) Critical Value: invNorm(.05): -1.64 P2 = (73-75)-0 75(1- 1-.75)(1926 2011) 1508 2011 = .75 =-1.43 Test Statistic 65122 06
University officials hope that changes they have made have improved the retention rate. In 2010, a sample of 1926 freshmen showed that 1400 returned as sophomores. In 2011, 1508 of 2011 freshmen sampled retumed as sophomores. Determine if there is sufficient evidence at the 0.05 level to say that the retention rate has improved. Ho: P1 = P2 H₁: P₁ P2 p = x₁+x2 = n₁+n₂ Z= P₁ = 1400 1926 1400+1505 1926+2011 =.73 2905 3937 Z= = .74 (P1-P2)-(P1-P2) √(1-P)(²+1) Critical Value: invNorm(.05): -1.64 P2 = (73-75)-0 75(1- 1-.75)(1926 2011) 1508 2011 = .75 =-1.43 Test Statistic 65122 06
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:University officials hope that changes they have made have improved the retention rate. In
2010, a sample of 1926 freshmen showed that 1400 returned as sophomores. In 2011, 1508 of
2011 freshmen sampled returned as sophomores. Determine if there is sufficient evidence at the
0.05 level to say that the retention rate has improved.
und.
Ho: P₁ = P2
H₁: P₁ P2
p
ô =
p =
XIE
Z =
n
X1+x2
n₁+n₂
=
P₁
=
1400
1926
1400+1505
1926+2011
= .73
2905
3937
Z =
= .74
(P1-P2)-(P1-P₂)
√p(1-P)(²+2)
Critical Value: invNorm(.05): -1.64
(73-.75)-0
75(1-.75)(1926 2011)
P₂ =
p-value: 0.0505 or on table at -1.64
0.0505 > 0.05 Fail to Reject
10552
1508
2011
= .75
-1.43 Test Statistic
964
Conclusion: There is sufficient evidence at the 0.05 level of significance to support the
university's claim that the retention rate improved between 2010 and 2011.
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