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.
H0 – population proportion p = 0.26 H1 – population proportion p > 0.26
Calculate z-value for test statistics
Use attached Table A-2 for Normal Distribution to find p-value. At the significance level 0.05 make decision: reject or do not reject H0.
8. Hypothesis test of a single population mean. Null Hypothesis Ho: μ = 500
Alternative Hypothesis H1: 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.
For # 9, 10, 11, 12 use data from the table below:
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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