| 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. | |
(5)
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. | |
(5)
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. | |
(4)
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. | |
(3)
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. | |
(5)
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. | |
(7)
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. | |
(4)
b) the tail probability or p-value is P(z > 1.945) = 0.5 - 0.4744 = 0.0256.
(2)
c) Since 
(2)
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. | |
(6)
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. | |
(7)
TOTAL (50)
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