Question 5:
5 | (a) | H : distributions of ages for urban and rural areas
0
are identical; H : distributions differ as to median
1
Or H : m = 0, H : m > 0, where m is the median
0 d 1 d d
of population differences of age of marriage for
men in urban and rural areas
or H : population median ages in urban & rural areas
0
are equal, H : median age higher in urban areas
1
Rankings of rural ages are 1, 2, 4, 7, 9, 11
R = 34 and m(m + n + 1) – R = 56
m m
W = 34
CV 31
34 > 31 so do not reject H , or 0.0876 > 0.05
0
Insufficient evidence that average ages are higher | B1
M1
B1
A1
B1
M1ft
A1ft
[7] | 1.1
3.1b
1.1
1.1
1.1
1.1
2.2b | If “distributions identical”, allow any type of average.
If not “distributions identical” then must use median.
Allow use of m and m, provided they are defined as median, or entirely
u r
verbal (see below) but need some context
Find rankings of rural ages within whole sample, can be implied by 34
Consider m(m + n + 1) – R (if omitted, can get all other marks)
m
Correct W, allow p = 0.0876 from N(45, 60) with cc
Correct CV used, allow 31 or 31.76 from N(45, 60)
Comparison and correct first conclusion, needs correct method for R .
m
FT on their 34, but not 56, and on 29 instead of 31 but no other CV except
FT on wrong m or n (e.g. m = 5, CV 23 which gets B1M1B0A1B0M1A1)
Contextualised, not over-assertive, not “significant evidence that average
ages are the same”. Same ft. Allow “different”.
If from valid method their W  31, so that conclusion changes, FT for (a) (“significant evidence that average ages are different”) and consult PE if (b) is problematic
(b) | 1 + 2 + 4 + 7 + 8 + 10 = 32 | M1
A1 | 3.1b
1.1 | Attempt to change total to 32 (or 30 if CV 29 used), e.g. 8 seen
Find age that makes rank sum of 32 (or 31 if 29 used – can’t get 30??)
(M1A1 can be implied by answer of 20/0, allow 19/12)
OR | T&I: Test at least two new ages and find R for each
m | M1
19/10 or 20/0 or 19/12 stated | A1
11th becomes 7th so least age of Mr X is 19/10 | A1
[3] | 3.2a | (old 11th becomes new 7th, old 7th becomes new 8th)
Condone absence of working.
A | H : median in urban & rural areas are equal, H : median higher in urban areas (no context – needs “ages” as a minimum)
0 1 | B0
B | H : average ages in urban & rural areas are equal, H : average age higher in urban areas (minimum context, but “average” not median”)
0 1 | B0
C | H : median ages in urban & rural areas are equal, H : median age higher in urban areas (condone omission of “population”)
0 1 | B1
D | H : median of differences in ages is 0, H : greater than 0 (BOD for their meaning “urban minus rural” rather than “rural minus urban”)
0 1 | B1
E | H : m = m, H : m > m where m and m are the median ages of marriage for men in urban and rural districts respectively
0 u r 1 u r u r | B1