## Lesson 17: Inference for Proportions

October 26, 2016

Wed, Oct 26

Review:

- Estimation with Confidence Intervals

Presentation:

- How to Estimate a Population Proportion
- Conduct a Simple Random Sample (SRS) of size
*n* - Record the count,
*x*, of “successes”, e.g., # of voters supporting candidate A - Calculate the sample proportion,
*p-hat = x/n* - If
*n*is sufficiently large (≥30), we can assume*p-hat*is Normally distributed - Estimate of the population proportion mean,
*μ = p-hat* - Estimate of the population proportion std dev,
*σ = √(p*(1-p)/n)* - Estimate margin of error,
*m = z*σ*(use*z = 1.96 for 95% confidence)* - Estimate with 95% confidence interval is
*p-hat ± m*

- Conduct a Simple Random Sample (SRS) of size
- Example 8.1 on p. 489
*n*= 13,819*x*= 3,140*p-hat*=*x/n*= 3,140/13,819 = 0.227- Standard Deviation =
*√(p*(1-p)/n) =*√(0.227*(1-0.227)/13,819) = 0.00356 - m =
*z*σ =*1.96*0.00356 = 0.00698 - p-hat ± m = 0.227 ± 0.00698
- 95% CI = [0.22002, 0.23398]

Activity:

- Complete Problems 8.1 and 8.2 on p. 490-491
- Election Polling Questions
- In a survey conducted by Quinnipiac University (October 10-17), 685 likely Colorado voters were asked which candidate for President they plan to vote for in the election. The candidates and corresponding support levels are listed below. Calculate a 95% confidence interval for each candidate.
- Clinton 45%
- Trump 37%
- Johnson 10%
- Stein 3%

- In a poll conducted in September by Colorado Mesa University and Rocky Mountain PBS, 540 registered voters were asked whether they favor or oppose Amendment 70 (increasing the Colorado minimum wage) with the following results. Calculate a 95% confidence interval for the “Favor” and “Oppose” proportions.
- Favor 58%
- Oppose 36%
- Undecided 7%

- In a survey conducted by Quinnipiac University (October 10-17), 685 likely Colorado voters were asked which candidate for President they plan to vote for in the election. The candidates and corresponding support levels are listed below. Calculate a 95% confidence interval for each candidate.

Assignment:

- Read pp. 487-491, Inference for Proportions
- Read two recent FiveThirtyEight.com articles by Nate Silver