Question

A systematic random sample was taken from the set of all Presidents of the United States. The data file potus heights.csv random sample includes the height (in inches) of each sampled President. (a) From this data, estimate the average height of United States Presidents. Calculate two error bounds for your estimate, one using the usual SRS formula, and one using the successive difference variance estimator. (b) Which variance estimator is more appropriate for these data? Briefly explain

president	hgt
Van Buren	56
McKinley	57
Harrison	68
Carter	69
Roosevelt	70
Cleveland	71
Buchanan	72
Kennedy	72
AJackson	73
GHWBush	74
Lincoln	76

Answer 1

president	hgt
Van Buren	56
McKinley	57
Harrison	68
Carter	69
Roosevelt	70
Cleveland	71
Buchanan	72
Kennedy	72
Ajackson	73
GHWBush	74
Lincoln	76
Average height of United states president=					68.90909
variance=	38.80992	Standard deviation=		6.229761
using normality asumption for simple srs we can compute error bounds
(68.9090-6.2297/sqrt(11))*1.96)			and	(68.9090+(6.2297/sqrt(11))*1.96)
65.22748	and	72.59052		at 5% los
method 2
successive difference variance method
variance =	(1-1/n)*σ2 =		35.28175	and	STANDARD Deviation=			5.939844
using normality asumption we can obtain bounds
(68.9090-(5.9398/sqrt(11))*1.96)				and	(68.9090+(5.9398/sqrt(11))*1.96)
65.3988	and	72.4192		at 5% los
b) successive difference variance estimator is more appropriate for this data