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(a) Observed Frequencies: X Y Z Total A 20 44 34 98 B 17 34 21 72 Total 37 78 55 170 Expected Frequencies: Observed Frequencies: X Y Z Total A 37X98/170=2133 44.96 31.71 98 B 15.67 33.04 23.29 72 Total 37 78 55 170 (b) O E (O - E)2/E 20 21.33 0.0829 44 44.96 0.0205 34 31.71 0.1654 17 15.67 0.1129 34 33.04 0.0279 21 23.29 0.2252 Total = = 0.636 Test statistic = = 0.636 (c) = 0.10 ndf = (r - 1) X (c - 1) = (2 - 1)X (3 - 1) = 2 From Table, critical value of = 4.605 (d) Since the calculated value of = 0.636 is less than critical value of = 4.605, the difference isnot significant. Fail to reject null hypothesis. Conclusion: Correct option: There is not sufficient evidence to support the claim that the row and column variables are dependent.

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g = GM / r² Where g is the acceleration due to gravity, G is the gravitational constant (6.67x10^-11), M is the mass of the object (kg) and r is the radius (m). g = (6.67*10^-11)*(1.9*10^27) / (6.99*10^7)² = 25.94 m/s² This is roughly the actual surface acceleration on Jupiter.

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