STATISTICS TEST # 3A SOLUTIONS

Show your work and the formulae you use:

1)
 z -Curve Hypothesis Test on a Mean Ho: l = 55 Ha: l > 55 Level of significance: a = 5 % Criteria: if z > 1.645, reject Ho Statistic: Conclusion: we cannot reject the null hypothesis Ho.

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2)
 Student-t Curve Hypothesis Test on 2 Means Ho: l1 = l2 Ha: l1 ! l2 Level of significance: a = 5 % Criteria: if | t | > 2.086, reject Ho Statistic: Conclusion: we must reject the null hypothesis Ho.

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3) a)
 Hypothesis Test on Proportion Ho: p = 0.20 Ha: p ! 0.20 Level of significance: a = 1 % Criteria: if z > 2.575, reject Ho Statistic: Conclusion: we cannot reject the null hypothesis Ho.

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b)
 Hypothesis Test on Proportion Ho: p [ 0.20 Ha: p > 0.20 Level of significance: a = 1 % Criteria: if z > 2.33, reject Ho Statistic: Conclusion: we must reject the null hypothesis Ho.

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4)
 Hypothesis Test on Difference of Proportions Ho: p 1 = p 2 Ha: p 1 ! p 2 Level of significance: a = 5 % Criteria: if | z | > 1.96, reject Ho Statistic: Conclusion: we cannot reject the null hypothesis Ho.

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5)
 Name Before After differences statistics Marcia 18 30 12 Nevin 38 70 32 Marie-Josée 8 20 12 Bob 10 4 -6 r d = 13.37 Steward 12 10 -2 Tammy 12 20 8

 t-Curve Hypothesis Test on Differences Ho: l d = 0 Ha: l d ! 0 Level of significance: a = 10 % Criteria: if | t | > 2.015, reject Ho Statistic: Conclusion: we cannot reject the null hypothesis Ho.

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6) a)
 Hypothesis Test on Difference of Means Ho: l1 = l2 Ha: l1 > l2 Level of significance: a = 1 % Criteria: if z > 2.33, reject Ho Statistic: Conclusion: we cannot reject the null hypothesis Ho.

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b) the tail probability or p-value is P(z > 1.945) = 0.5 - 0.4744 = 0.0256.

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c) Since

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7)
 Hypothesis Test on Mean Ho: l [ 15 Ha: l > 15 Level of significance: a = 5 % Criteria: if t > 1.753, reject Ho Statistic: Conclusion: we must reject the null hypothesis Ho.

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8)
 Chi Square Hypothesis Test Ho: student's grade is independent of prof Ha: student's grade dependent on prof Level of significance: a = 1% Criteria: if x 2 > 13.277 heave Ho. Statistic: Conclusion: we must reject Ho. It seems a studen'ts grade depends on the prof.

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TOTAL (50)

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