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A systematic random sample was taken from the set of all Presidents of the United States....

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Basic Math

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

presidenthgt
Van Buren56
McKinley57
Harrison68
Carter69
Roosevelt70
Cleveland71
Buchanan72
Kennedy72
AJackson73
GHWBush74
Lincoln76

Answer & Explanation Solved by verified expert
3.8 Ratings (719 Votes)

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
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