Misc. Calculus Problems

1. What is the point estimate of the true proportion of people who wear hearing aids if, in a random sample of 676 people, 35 people had hearing aids? (Points : 6) 0.050 0.052 0.948 0.049 Question 2. 2. The following confidence interval is obtained for a population proportion, p:(0.499, 0.525). What is the point estimate, pq5_7? (Points : 6) 0.525 0.499 0.518 0.512 Question 3. 3. The following confidence interval is obtained for a population proportion, p:0.332 < p < 0.372. What is the margin of error, E? (Points : 6) 0.040 0.352 0.020 0.021 Question 4. 4. What is the critical value e3_1 that corresponds to a level of confidence of 98%? (Points : 6) 2.575 1.75 2.05 2.33 Question 5. 5. What is the margin of error for the 95% confidence interval used to estimate the population proportion, given that n = 184 and x = 93? (Points : 6) 0.0722 0.0650 0.00266 0.126 Question 6. 6. In a clinical test with 2219 subjects, 70% showed improvement from the treatment. What is the margin of error for the 95% confidence interval used to estimate the population proportion? (Points : 6) 0.0191 0.0254 0.0211 0.0160 Question 7. 7. In a survey of 3000 T.V. viewers, 40% said they watch network news programs. What is the margin of error for the 95% confidence interval used to estimate the population proportion? (Points : 6) 0.0131 0.0201 0.0230 0.0175 Question 8. 8. What is the minimum sample size you should use to assure that your estimate of pq5_7 will be within the required margin of error around the population p? Margin of error: 0.018; confidence level: 99%; and e3_18 are unknown. (Points : 6) 36 72 1 5117 Question 9. 9. What is the minimum sample size you should use to assure that your estimate of pq5_7 will be within the required margin of error around the population p? Margin of error: 0.04; confidence level: 95%; from a prior study, pq5_7 is estimated by the decimal equivalent of 94%. (Points : 6) 136 120 5 408 Question 10. 10. Use the confidence level and sample data to find the margin of error E. Replacement times for washing machines: 90% confidence; n = 33, e3_29 = 11.2 years, sigma σ = 2.3 years. (Points : 7) 0.7 years 0.1 years 5.7 years 0.5 years Question 11. 11. A random sample of 107 light bulbs had a mean life of e3_29 = 590 hours with a standard deviation of sigma σ = 27 hours. Construct a 90 percent confidence interval for the mean life, μ, of all light bulbs of this type. 583 < μ < 597 585 < μ < 595 584 < μ < 596 586 < μ < 594 (Points : 7) Please refer to answer choice a. above. Please refer to answer choice b. above. Please refer to answer choice c. above. Please refer to answer choice d. above. Question 12. 12. Do one of the following, as appropriate: Find the critical value e3_1, find the critical value pq5_3, or state that neither the normal nor the t distribution applies. 91% level of confidence; n = 45; sigma σ is known; population appears to be very skewed. e3_1 = 1.75 e3_1 = 1.70 pq5_3 = 1.34 pq5_3 = 1.645 (Points : 7) Please refer to answer choice a. above. Please refer to answer choice b. above. Please refer to answer choice c. above. Please refer to answer choice d. above. Neither the normal nor the t distribution applies Question 13. 13. A random sample of 90 full-grown lobsters had a mean weight of 18 ounces and a standard deviation of s=2.8 ounces. Construct a 98 percent confidence interval for the population mean μ. 17 < μ < 19 18 < μ < 20 17 < μ < 20 16 < μ < 18 (Points : 6) Please refer to answer choice a. above. Please refer to answer choice b. above. Please refer to answer choice c. above. Please refer to answer choice d. above. Question 14. 14. Find the margin of error given 95% confidence interval; n = 91 ; e3_29 = 26, s = 12.3. (Points : 6) 5.27 2.71 3.01 2.56 Question 15. 15. Use the given level of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. n = 10, e3_29 = 8.0, s = 2.5, 95 percent. 6.24 < μ < 9.76 6.21 < μ < 9.79 6.17 < μ < 9.93 6.55 < μ < 9.45 (Points : 6) Please refer to answer choice a. above. Please refer to answer choice b. above. Please refer to answer choice c. above. Please refer to answer choice d. above. Question 16. 16. Use the margin of error, confidence level, and standard deviation σ to find the minimum sample size required to estimate an unknown population mean μ. Margin of error: $125, confidence level: 95%, sigma σ = $524. (Points : 7) 2 68 5 59