Module 2 Homework Assignment 1. 459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours. Solution: 291/459 = 0.63 Instructor Comments: 2. Find the critical value for z/2 that corresponds to a degree of confidence of 98%. Solution: Instructor Comments: 3. Find the margin of error for the 95% confidence interval used to estimate the population proportion with n = 163 and x = 96. Solution: p = x/n = 96/163 = 0.59 Confidence coefficient is the critical value of z for 95% confidence = 1.96 Standard error of p = sqrt [p*(1-p)/n] = sqrt [0.59*0.41/163] = 0.0385 Margin of error = 1.96*0.0385 = 0.0755 Instructor Comments: 4. Construct the confidence interval for question 3. Solution: Instructor Comments: 5. Interpret the confidence interval found in question 4. Solution: Instructor Comments: 6. What are the requirements for a Student's t-distribution? Solution: Instructor Comments: 7. Find the critical value for t/2 corresponding to n = 12 and 95% confidence level. Solution: Instructor Comments: 8. Use the confidence level and sample data to find the margin of error E. College students' annual earnings: 99% confidence, n = 81, Solution: x = $3967, s = $874 Instructor Comments: 9. Construct the confidence interval for question 8 above. Solution: Instructor Comments: 10. Interpret the confidence interval found in question 9. Solution: Instructor Comments