STAT 528
HOMEWORK #6
Due: Noon Tuesday, November 3, 2015.
1. Consider the Fall Headcount Enrollment data.
Administrator #1 wants to determine if there were any significant shifts in the mean retention
percentage over the 24 academic years. She suggests using µ0 = 88% because she found that
value published in a research article and represents the average retention rate for all universities
in the Rocky Mountain region that have over 5000 undergraduate students. The standard
deviation σ is unknown and will be estimated using the MSSD. The goal is to detect a 1σ
shift in the mean retention rate using a cusum chart with h = 4 and k = .5.
(a) (.5pt) What is the value of the MSSD estimate of σ?
(b) (2pt) Generate a two-sided cusum plot and the two one-sided cusum plots.
(c) (1pt) For which years are out-of-control signals indicated (assuming the cusum is reset
after each out-of-control signal). Also indicate if a signal occurs on the lower or upper
side.
(d) (1.5pt) Estimate the magnitude of the first significant shift that occurs and indicate the
sample on which the shift began.
2. (5pt) Administrator #2 decides to use estimate µb 0 = 88.653 which is the mean retention rate
for these 24 years. Rework Problem #1 with µb 0 = 88.653
The following SAS code will be sent to you.
DATA in;
INPUT year fall spring retained
LINES;
2014 2943 2590 88.0
2013 2921 2558
2012 2710 2404 88.7
2011 2669 2358
2010 2623 2355 89.8
2009 2316 2060
2008 2070 1826 88.7
2007 2105 1837
2006 2216 1930 87.1
2005 2236 1960
2004 2184 1925 88.1
2003 2165 1917
2002 2120 1878 88.6
2001 1894 1688
2000 2032 1814 89.2
1999 2025 1816
1998 2041 1820 89.2
1997 1998 1767
1996 1932 1727 89.4
1995 1893 1686
1994 1791 1562 87.2
1993 1817 1628
1992 1613 1429 88.6
1991 1527 1373
;
SYMBOL1 v=dot width=3;
PROC SORT DATA=in; BY year;
@@;
87.6
88.3
88.9
87.3
87.6
88.5
89.1
89.7
88.4
89.1
89.6
89.9
RUN;
3. (1.5pt) Find ARL0 and ARL1 in 1. and 2. if a FIR of H/2 is used. Would you recommend
one of these plans over the other? Why or why not?
4. (1pt) Provide h and k values for a CUSUM that has an on-aim ARL close to 360 and an ARL
of less than 6 when a 1.5σ shift has occurred.
5. (2pt) Exercise 9.9, page 431. Assume the goal is to quickly detect a ∆ = .5σ shift in the
mean.
6. (2pt) Exercise 9.14, page 431.