1 / 19

Confidence Intervals about a Population Proportion Section 8.3

2. Objectives 8.3. Obtain a point estimate for the population proportionObtain and interpret a confidence interval for the population proportionDetermine the sample size for estimating a population proportion. 3. Point Estimate of a Population Proportion. Suppose a simple random sample of size n i

tave
Download Presentation

Confidence Intervals about a Population Proportion Section 8.3

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. Confidence Intervals about a Population Proportion Section 8.3 Alan Craig 770-274-5242 acraig@gpc.edu

    2. 2 Objectives 8.3 Obtain a point estimate for the population proportion Obtain and interpret a confidence interval for the population proportion Determine the sample size for estimating a population proportion

    3. 3 Point Estimate of a Population Proportion Suppose a simple random sample of size n is obtained from a population in which each individual either does or does not have a certain characteristic. The best point estimate of p, denoted , the proportion of the population with a certain characteristic, is given by where x is the number of individuals in the sample with the specified characteristic.

    4. 4 Example: #8 (a), p. 374 A study of 74 patients with ulcers was conducted in which they were prescribed 40 mg of Pepcid. After 8 weeks, 58 reported confirmed ulcer healing. (a) Obtain a point estimate for the proportion of patients with ulcers receiving Pepcid who will have confirmed ulcer healing.

    5. 5 Example: #8 (a), p. 374 A study of 74 patients with ulcers was conducted in which they were prescribed 40 mg of Pepcid. After 8 weeks, 58 reported confirmed ulcer healing. (a) Obtain a point estimate for the proportion of patients with ulcers receiving Pepcid who will have confirmed ulcer healing.

    6. 6 Sampling Distribution of For a simple random sample of size n such that n = .05N (i.e., sample size is no more than 5% of the population), the sampling distribution of is approximately normal with mean and standard deviation provided that np(1-p) = 10.

    7. 7 For a simple random sample of size n, a (1-a) 100% confidence interval for p is given by provided that np(1-p) = 10. Constructing a (1-a) 100% Confidence Interval for a Population Proportion

    8. 8 Example: #8, (b), p.374 (b) Verify that the requirements for constructing a confidence interval about are satisfied. What do we need to do?

    9. 9 (b) Verify that the requirements for constructing a confidence interval about are satisfied. We must show that np(1-p) = 10. 74 * 0.784 * (1 - 0.784) = 12.53 > 10 Example: #8, (b), p.374

    10. 10 (c) Construct a 99% confidence interval for the proportion of patients with ulcers receiving Pepcid who will have confirmed ulcer healing. Example: #8, (c), p.374

    11. 11 (c) Construct a 99% confidence interval for the proportion of patients with ulcers receiving Pepcid who will have confirmed ulcer healing. Example: #8, (c), p.374

    12. 12 Construct a 99% confidence interval for the proportion of patients with ulcers receiving Pepcid who will have confirmed ulcer healing. Using Calculator: STAT?TESTS?A: 1-PropZInt Enter 58 for x, 74 for n, and .99 for C-Level Example: #8, (c), p.374

    13. 13 Margin of Error ? Sample Size Solving margin of error to find sample size gives

    14. 14 Margin of Error ? Sample Size So we can use a prior estimate for p, or we can find the largest value of . Using the fact that this is a parabola that opens down (see Figure 17 p. 373), we can find the y-coordinate of the vertexthat is its maximum value Alternatively, we can use Calculus to find the maximum value. In either case = 0.25, so

    15. 15 The sample of size needed for a (1-a) 100% confidence interval for p with a margin of error E is given by (rounded up to next integer) where is a prior estimate of p. If a prior estimate of p is unavailable, the sample size required is Sample Size for Estimating the Population Proportion p

    16. 16 (a) he uses a Census Bureau estimate of 67.5% from the 4th quarter of 2000? (b) he does not use any prior estimates? Example: # 16, p. 375

    17. 17 Example: # 16, p. 375 within 2 percentage points with 90% confidence if (a) he uses a Census Bureau estimate of 67.5% from the 4th quarter of 2000?

    18. 18 Example: # 16, p. 375 within 2 percentage points with 90% confidence if (b) he does not use any prior estimates?

    19. 19 Questions ???????????????

More Related