STAT200 QUIZ-3 Write your solutions on a separate paper. 1. Consider a trial where a person is charged with a crime. The Null Hypothesis is that the defendant is not guilty. Describe Type I and Type II Errors. 2. Imagine performing a hypothesis test if an average score on the Final Exam is 16 points. Setup Ho and Ha for 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 = 0.05. 4. Use attached Table A-2 for Normal Distribution to find p-value for a Left-Tailed test with test statistics z = - 1.12. 5. Use attached Table A-3 for t-Distribution to find the critical t value for Left-Tailed test with sample size = 20 and significance level = 0.01. 6. The P-value of a hypothesis test is 0.008. Which of the following claims is correct? Explain the answer. 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. For #7 and #8 apply p-value method for the testing population proportion: Evaluate the claim that percent of new small businesses (population proportion) survived 5 years is less than 40%. H0 - population proportion p = 0.4 H1 - population proportion p < 0.4 Sample of N=80 new small businesses were checked after 5 years and found that 30 of them survived. 7. Calculate z-value for the test statistics. Tip: in case of population proportion, test statistics is calculated by formula ( ps p) z= p (1 p) N p is a population proportion, taken from Ho, N - sample size. ps is a sample proportion, calculated as a number of survived businesses divided by the sample size N. 8. Use attached Table for Normal Distribution to find p-value. At the significance level 0.05, apply p-value to make the decision: reject or do not reject H0. Explain your decision. For #9 and #10 apply critical value (rejection region) method for the following Hypothesis testing of a single population mean: 9. Null Hypothesis Ho: = 200 Alternative Hypothesis H1: 200 (Two-Tailed test) In a random sample of 100 subjects, the sample mean found to be x =220. Population standard deviation is =50. Significance level is = 0.10 Calculate test statistics For the given significance level = 0.10, find critical values (use attached table for Normal Distribution) 10. Draw the line for z-scale and use critical values to identify rejection region (shade these portions) Mark position of test statistics on your z-scale. Does test statistics fall in the rejection region? Will you reject or do not reject Ho? For #11 and 12 use table below: 11. 12. x y 2 9 5 15 7 20 10 18 16 28 Calculate Coefficient of Linear Correlation. Find the equation of Regression Line