**STAT200 QUIZ-3**

**1.***Consider a trial where a person is charged with a crime.
The Null Hypothesis is that the defendant is not guilty.
Identify following verdicts as Type I or Type II Errors:
a) Person committed crime, b court failed to prove it and found him not guilty.
b) Court found the person guilty for the crime that he actually did not commit. *

**2.***Imagine performing a hypothesis test if an average age of college graduates is 31 years old.
Will it be Left-Tailed, Right-Tailed or Two-Tailed test?*

**3. ***Use attached Table A-2 for Normal Distribution to find the critical z value for Right-Tailed test with significance level α = 0.15.*

**4. ***Use attached Table A-3 for t-Distribution to find the critical t value for Left-Tailed test with sample size = 21 significance level α = 0.01.*

**5. ***Use attached Table A-2 for Normal Distribution to find p-value for a Left-Tailed test
with test statistics z = – 1.12.*

**6.***The P-value of a hypothesis test is 0.0345.
Which of the following claims is correct?*

*A) Reject Ho at the 0.05 significance level but not the 0.01 significance level.*

*B) Reject Ho at the 0.01 significance level but not the 0.05 significance level.*

*C) Reject Ho at both the 0.01 significance level and the 0.05 significance level.*

*D) Do not reject Ho at significance level 0.01 and do not reject Ho at the 0.05 significance level.*

**7.*** Testing Claim about a Proportion.
Evaluate the claim that percent of small businesses closed this year (population proportion) is greater than 26%. Sample of 500 small businesses were taken all over the country and 145 of them were closed this year. *

*H _{0} – population proportion p = 0.26
H_{1} – population proportion p > 0.26*

* Calculate z-value for test statistics*

** ***Use attached Table A-2 for Normal Distribution to find p-value.
*

**8. ***Hypothesis test of a single population mean.
Null Hypothesis Ho: μ = 500*

*Alternative Hypothesis H _{1}: μ ≠ 500 (Two-Tailed test)*

*In a random sample of 64 subjects, the sample mean found to be x=490.
Population standard deviation is σ=40. *

*Calculate test statistics and find P-value for this test (use attached table A-2).
With significance level α = 0.1 make the decision: reject or do not reject (accept) Ho.
Show basic steps of Hypothesis Testing.*

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**For # 9, 10, 11, 12 use data from the table below:**

** **

x | y | x^{2} |
y^{2} |
xy |

2 | 18 | |||

4 | 25 | |||

6 | 22 | |||

8 | 30 | |||

10 | 32 | |||

Σx= | Σy= | Σx^{2}= |
Σy^{2}= |
Σ(xy)= |

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* *

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**9. *** **Complete the table. Fill in all columns and calculate sums in the last row.*

**10. ***Use results from #9 and calculate Pearson Coefficient of Linear Correlation.*

**11. **** ***Use results from #9 and calculate slope of Linear Regression Line.*

**12. ** *Use results from #9 and calculate y-intercept of Linear Regression Line.
Write an equation of Regression Line.*

* *

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