Question

In: Math

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

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

Expert Solution

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

milcah answered 9 months ago

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