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Section 8.1

Learn how to determine the sample size for a survey with a maximum 2% margin of error and 90% confidence level. Practice constructing confidence intervals based on sample data.

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Section 8.1

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  1. Section 8.1 Day 4

  2. What sample size should you use for a survey if you want the margin of error to be at most 2% with 90% confidence?

  3. What sample size should you use for a survey if you want the margin of error to be at most 2% with 90% confidence?

  4. What sample size should you use for a survey if you want the margin of error to be at most 2% with 90% confidence? Because no estimate of p, use p = 0.5

  5. What sample size should you use for a survey if you want the margin of error to be at most 2% with 90% confidence? Because no estimate of p, use p = 0.5 n =(1.645)2●(0.5)(1 – 0.5)/(0.02)2

  6. What sample size should you use for a survey if you want the margin of error to be at most 2% with 90% confidence? Because no estimate of p, use p = 0.5 n =(1.645)2●(0.5)(1 – 0.5)/(0.02)2 n =1691.266

  7. What sample size should you use for a survey if you want the margin of error to be at most 2% with 90% confidence? Because no estimate of p, use p = 0.5 n =(1.645)2●(0.5)(1 – 0.5)/(0.02)2 n =1691.266 n = 1692

  8. Page 487, E7 A sample of 549 randomly selected teenagers ages 13 – 17 were asked whether it is appropriate for parents to install a computer program limiting what teens can access on the Internet. Fifty-two percent responded that, yes, this was an appropriate measure. Check the conditions and then construct a 90% confidence interval of the proportion of teenagers nationwide who would think this is an appropriate measure.

  9. Check Conditions

  10. Check Conditions a) (1) Problem states this is a random sample.

  11. Check Conditions a) (1) Problem states this is a random sample. (2) Both np = 549(0.52) = 285.48 and n(1-p) = 549(0.48) = 263.52 are more than 10.

  12. Check Conditions a) (1) Problem states this is a random sample. (2) Both np = 549(0.52) = 285.48 and n(1-p) = 549(0.48) = 263.52 are more than 10. (3) There are more than 10(549) = 5,490 teenagers aged 13 to 17 in the United States.

  13. 90% Confidence Interval

  14. 90% Confidence Interval A sample of 549 randomly selected teenagers ages 13 – 17 were asked whether it is appropriate for parents to install a computer program limiting what teens can access on the Internet. Fifty-two percent responded that, yes, this was an appropriate measure. Check the conditions and then construct a 90% confidence interval of the proportion of teenagers nationwide who would think this is an appropriate measure.

  15. 90% Confidence Interval 1-PropZInt x = 286 x = 52% of 549 = 285.48 n = 549 C-level: .90 Remember, x must be a whole number

  16. 90% Confidence Interval 1-PropZInt x = 286 x = 52% of 549 n = 549 C-level: .90 (.48588, .55602)

  17. (c) What is it that you are 90% sure is in the confidence interval?

  18. Page 487, E7 A sample of 549 randomly selected teenagers ages 13 – 17 were asked whether it is appropriate for parents to install a computer program limiting what teens can access on the Internet. Fifty-two percent responded that, yes, this was an appropriate measure. Check the conditions and then construct a 90% confidence interval of the proportion of teenagers nationwide who would think this is an appropriate measure.

  19. (c) What is it that you are 90% sure is in the confidence interval? Construct a 90% confidence interval of the proportion of teenagers nationwide who would think this is an appropriate measure.

  20. (c) What is it that you are 90% sure is in the confidence interval? the proportion of teenagers nationwide who would think it is appropriate for parents to install a computer program limiting what teens can access on the Internet

  21. (d) Interpret this confidence interval (in context).

  22. (d) Interpret this confidence interval (in context). I am 90% confident that the proportion of all teenagers nationwide who would think it is appropriate for parents to install a computer program limiting what teens can access on the Internetis between 48.6% and 55.6%.

  23. (e) Explain the meaning of 90% confidence.

  24. (e) Explain the meaning of 90% confidence. Suppose we could take 100 random samples from this population and construct the 100 resulting confidence intervals. We’d expect that the true proportion of all teenagers nationwide who would think it is appropriate for parents to install a computer program limiting what teens can access on the Internet would be in 90 of these intervals.

  25. Use only the chart of reasonably likely outcomes to answer parts a and b for this question. Do not use a formula or calculator.

  26. According to a recent report, about 70% of adults plan to vote in the next election. How many voters is it reasonably likely to get in a sample of 40 randomly selected adults?

  27. According to a recent report, about 70% of adults plan to vote in the next election. How many voters is it reasonably likely to get in a sample of 40 randomly selected adults? 22 to 34 adults

  28. Suppose that in a random sample of 40 students, 32 studied for a test. Find the 95% CI for the proportion of students who study for tests.

  29. Suppose that in a random sample of 40 students, 32 studied for a test. Find the 95% CI for the proportion of students who study for tests. (0.65, 0.90)

  30. Page 484, P11(a) In a survey consisting of a randomly selected national sample of 600 teens ages 13-17, 4% of the 600 students responding gave their school a D rating (on a scale of A, B, C, D, F). (a) Check to see if the three conditions for computing a confidence interval are met in this case. (Need to be specific, not just general here)

  31. Page 484, P11(a) In a survey consisting of a randomly selected national sample of 600 teens ages 13-17, 4% of the 600 students responding gave their school a D rating (on a scale of A, B, C, D, F). The problem states that the sample was selected randomly from all U.S. teens ages 13 to 17.

  32. Page 484, P11(a) In a survey consisting of a randomly selected national sample of 600 teens ages 13-17, 4% of the 600 students responding gave their school a D rating (on a scale of A, B, C, D, F).

  33. Page 484, P11 In a survey consisting of a randomly selected national sample of 600 teens ages 13-17, 4% of the 600 students responding gave their school a D rating (on a scale of A, B, C, D, F). There are well over 600(10) = 6000 teens ages 13 to 17 in the United States. All three conditions are met.

  34. Page 484, P11(b) In a survey consisting of a randomly selected national sample of 600 teens ages 13-17, 4% of the 600 students responding gave their school a D rating (on a scale of A, B, C, D, F). (b) Find a 95% confidence interval for the percentage of all teenagers in the United States who would give their school a D rating.

  35. Page 484, P11(b) In a survey consisting of a randomly selected national sample of 600 teens ages 13-17, 4% of the 600 students responding gave their school a D rating (on a scale of A, B, C, D, F). (b) Find a 95% confidence interval for the percentage of all teenagers in the United States who would give their school a D rating.

  36. Page 487, E8 Conditions met?

  37. Page 487, E8 (1) There is no indication of how the sample was selected, so the random sample condition may not have been met

  38. Page 487, E8 (1) There is no indication of how the sample was selected, so the random sample condition may not have been met (2) np = 885(0.40) = 354 and n(1 – p) = 885(0.6) = 531 are both at least 10

  39. Page 487, E8 (1) There is no indication of how the sample was selected, so the random sample condition may not have been met (2) np = 885(0.40) = 354 and n(1 – p) = 885(0.6) = 531 are both at least 10 (3) There are more than 885(10) = 8850 adults nationwide So, two of the three conditions are met

  40. Page 487, E8 90% confidence interval is?

  41. Page 487, E8 90% confidence interval 1-PropZInt x: 354 n: 885 C-Level: .90

  42. Page 487, E8 (.37291, .42709) Of course, you can have confidence in this interval only if the sampling was done randomly.

  43. Questions?

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