Question

The Hill of Tara in Ireland is a place of great archaeological importance. This region has been occupied by people for more than 4,000 years. Geomagnetic surveys detect subsurface anomalies in the earth's magnetic field. These surveys have led to many significant archaeological discoveries. After collecting data, the next step is to begin a statistical study. The following data measure magnetic susceptibility (centimeter-gram-second ⨯ 10-6) on two of the main grids of the Hill of Tara (Reference: Tara: An Archaeological Survey by Conor Newman, Royal Irish Academy, Dublin). Grid E: x variable 21.91 19.32 33.01 15.62 37.82 36.71 18.58 7.11 35.60 36.34 35.23 20.06 21.54 35.23 Grid H: y variable 47.60 26.45 51.36 24.10 48.07 12.35 32.09 46.19 30.21 57.47 34.91 29.74 13.29 40.55 (a) Compute Σx, Σx2, Σy, Σy2. (Enter your answers to 2 decimal places.) Σx Σx2 Σy Σy2 (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Enter your answers to 2 decimal places.) x y x s2 s (c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Enter your answers to 2 decimal places.) x y Lower Limit Upper Limit

Answer 1

a)

Σx,=374.08

Σx2=11297.34,

Σy=494.38,

Σy2 =19950.10

b)

for x

sample mean=26.72,

variance=100.15,

and standard deviation =10.01

for y:

sample mean=35.31,

variance=191.70,

and standard deviation =13.85

c) 75% Chebyshev interval around the mean for x values =26.72-/+2*10.01=6.70 to 46.74

75% Chebyshev interval around the mean for y values =35.31-/+2*13.85=7.61 to 63.01