Confidence Interval Estimation

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Confidence Interval Estimation – Discussion

When the results of a survey or poll are published, the sample size and the margin of error are both given. For example: 1000 voters were surveyed and 39±2% of the voters agree with the president. In this example N=1000 and the margin of error (MoE) is 2%.

This website lists several public opinion polls. Search the site and find a poll where the sample size and margin of error are given. Try to find a poll dealing with a topic in your profession or one in which you are really interested.

http://www.pollingreport.com

Determine the following information for the selected poll results and include in your initial post:

  1. URL for the website. State the poll question, the sample size N, and the margin of error (also known as sampling error).
  2. Interpret the results of your poll using your own words and full sentences. Note: Depending on the question asked, your poll may have more than one poll result – you only need to discuss one result.
  3. State the confidence interval using the MoE. What does this confidence interval estimate?
  4. Use this worksheet (click to download CIE Proportion.xlsx) to calculate the confidence interval based on the sample size and the number of successes (the proportion you are interested in). Use a confidence level of 95%.
  5. What is the calculated confidence interval? How does this compare to the interval in part 3 using the poll’s MoE?
  6. Discuss potential biases that could skew sampling results.

See Example post.

First response: Choose a classmate’s post. Calculate the sample size needed for the given MoE and see if the poll had enough people surveyed. Use this worksheet (click to download Sample Size Proportion.xlsx) to find the sample size needed.

See Example post.

Second response: Choose another classmate’s post. Change the confidence level to 90% or 99%. What happened to the confidence interval (compared to your classmate’s)? Explain the change.

See Example post.

Unit 4 Discussion Example – Initial Post When the results of a survey or poll are published, the sample size and the margin of error are both given. For example: 1000 voters were surveyed and 39±2% of the voters agree with the president. In this example N=1000 and the margin of error (MoE) is 2%. This website lists several public opinion polls. Search the site and find a poll where the sample size and margin of error are given. Try to find a poll dealing with a topic in your profession or one in which you are really interested. http://www.pollingreport.com Determine the following information for the selected poll results and include in your initial post: 1. URL for the website. State the poll question, the sample size n, and the margin of error (also known as sampling error). 2. Interpret the results of your poll using your own words and full sentences. Note: Depending on the question asked, your poll may have more than one poll result – you only need to discuss one result. 3. State the confidence interval using the MoE. What does this confidence interval estimate? 4. Use worksheet (CIE Proportion.xlsx) to calculate the confidence interval based on the sample size and the number of successes (the proportion you are interested in). Use a confidence level of 95%. 5. What is the calculated confidence interval? How does this compare to the interval in part 3 using the poll’s MoE? 6. Discuss potential biases that could skew sampling results. ****************************************************************************************** 1) Opinions about Hydraulic Fracturing (“fracking”) were surveyed nationally during March 2016. These survey results can be found at: http://www.pollingreport.com/energy.htm The question posed was “"Do you favor or oppose hydraulic fracturing or 'fracking' as a means of increasing the production of natural gas and oil in the U.S.?” Sample size, n =1,019 adults nationwide. Margin of error ± 4. 2) 36% were in favor of fracking as a method for increasing our energy resources in the US 51% were opposed of fracking as a method for increasing our energy resources in the US 13% were unsure of their opinion on fracking for increasing our energy resources in the US 3) The confidence interval for each result is found by adding/subtracting the MoE from the result. In favor: (36 – 4%, 36 + 4%) = (32% - 40%) 4) & 5) Using CIE Proportion.xlsx, I will enter the following variables: n = 1019 Number of Successes = 36% of 1019 = 0.36*1019 = 366.84 rounded to 367 people Confidence Level = 95% Confidence Interval is (0.3307 – 0.3896) or (33.07% - 38.96%) Data Sample Size Number of Successes Confidence Level 1019 367 95% Intermediate Calculations Sample Proportion 0.360157 Z Value -1.9600 Standard Error of the Proportion 0.015038 Interval Half Width 0.0295 Confidence Interval Interval Lower Limit Interval Upper Limit 0.3307 0.3896 6) I can imagine many biases that would affect the results of this survey. The first bias might be in the selection of recipients of this survey. A selection bias might be present if the sample selection is not representative of the general population. A sampling error might be present as well as is what the margin of error represents, for this case, 4%. We do not know what organization sponsored the surveying process and analysis. If the sponsoring organization was a fracking company, this could present an ethical question about the results. These are just a few considerations for these survey results.
Unit 4 Discussion Example - First Response to a Classmate’s Post First response: Choose a classmate’s post. Calculate the sample size needed for the given MoE and see if the poll had enough people surveyed. Use worksheet (click to download Sample Size Proportion.xlsx) to find the sample size needed. ****************************************************************************************** Determining the sample size, n, needed for a given margin of error can be found by using the worksheet SampleSizeProportion.xlsx and the following variables: Estimate of true proportion = 0.36 Sampling error (also known as MoE) = 0.04 Confidence Level = 95% Data Estimate of True Proportion Sampling Error Confidence Level 0.36 0.04 95% Intermediate Calculations Z Value Calculated Sample Size Result Sample Size Needed -1.9600 553.1701 554 For a margin of error of 4%, the poll would need to sample at least 554 people only. Since the poll actually sampled over 1000 people, the survey results are appropriate.
Unit 4 Discussion Example - Second Response to a Classmate’s Post Second response: Choose another classmate’s post. Change the confidence level to 90% or 99%. What happened to the confidence interval (compared to your classmate’s)? Explain the change. ****************************************************************************************** Using the CIE Proportion.xlsx, I will enter the following variables: n = 1019 Number of Successes = 367 people Confidence Level = 90% Changing the level of confidence to 90%, gives us a slightly smaller confidence range: Confidence Interval at 90% (0.3354 – 0.3849) or (33.54% - 38.49%) as compared to the Confidence interval at 95% (0.3307 – 0.3896) or (33.07% - 38.96%) Data Sample Size Number of Successes Confidence Level Data 1019 Sample Size 367 Number of Successes 95% Confidence Level Intermediate Calculations Sample Proportion 0.360157 Z Value -1.9600 Standard Error of the Proportion 0.015038 Interval Half Width 0.0295 Confidence Interval Interval Lower Limit Interval Upper Limit 1019 367 90% Intermediate Calculations Sample Proportion 0.360157 Z Value -1.6449 Standard Error of the Proportion 0.015038 Interval Half Width 0.0247 Confidence Interval 0.3307 Interval Lower Limit 0.3896 Interval Upper Limit 0.3354 0.3849

Tutor Answer

mickeygabz
School: UIUC

See attached. I have already posted to the campus site.

Hello everyone.
For my Topic, I chose climate change since I am a firm believer in the protection of the
environment.
1. URL for the website. State the poll question, the sample size N, and the margin of error (also
known as sampling error).

URL: http://www.pollingreport.com/enviro.htm
Poll question: "Do you support or oppose Donald Trump's decision to withdraw
from the main international agreement that tries to address climate change?"
The poll was conducted by ABC News/Washington Post Poll on June 2-4, 2017.
N=527 adults nationwide. Margin of error = ± 5.
2. Interpret the results of your poll using your own words and full sentences. Note: Depending
on the question asked, your poll may have more than one poll result – you only need to
discuss one result.

The results of the ...

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