Sampling Error and Sample Size Calculation for Surveys
Learn how to compute sampling error and determine sample sizes for survey research. Understand the concepts of precision, confidence intervals, and margin of error in statistical sampling to enhance the accuracy of your survey results.
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1. Compute the sampling error - SRS Country 1 & 2 want to run a survey to estimate the car ownership and they have those information from the previous census. Can you tell them what they could expect in terms of sample precision? Popula- tion (N) Car Own- ership (p) Sam ple size (n) Expected standard error (e) Expected Margin of error (ME) Confidence interval 200 Country 1 2,000 50% 500 200 Country 2 1,000,000 50% 500
1. Compute the sampling error - SRS Country 1 & 2 want to run a survey to estimate the car ownership and they have those information from the previous census. Can you tell them what they could expect in terms of sample precision? Popula- tion (N) Car Own- ership (p) Sam ple size (n) Expected standard error (e) Expected Margin of error (ME) Confidence interval 200 3.5% 7.1% [42.9% ; 57.1%] Country 1 2,000 50% 500 2.2% 4.5% [45.5% ; 54.5%] 200 3.5% 7.1% [42.9% ; 57.1%] Country 2 1,000,000 50% 500 2.2% 4.5% [45.5% ; 54.5%]
2. Compute the sample size - SRS Country 1 & 2 want to run a survey to estimate the car ownership and they have those information from the previous census. Can you help them to compute the sample size given the expected standard error? Popula- tion (N) Car Own- ership (p) Expecte d standar d error (e) Sample size required (n) Adjusted sample size n(fpc) 2% Country 1 2,000 50% 5% 2% Country 2 1,000,000 50% 5%
2. Compute the sample size - SRS Country 1 & 2 want to run a survey to estimate the car ownership and they have those information from the previous census. Can you help them to compute the sample size given the expected standard error? Popula- tion (N) Car Own- ership (p) Expecte d standard error (e) Sample size required (n) Adjusted sample size n(fpc) 2% 625 476 Country 1 2,000 50% 5% 100 95 2% 625 624 Country 2 1,000,000 50% 5% 100 99
3. Compute sample size You have taken a break from your busy life as a NSO statistician to work as a consultant for Mr. Green s campaign for governor. He would like you to calculate the number of voters he would have to call to know how many voters plan to vote for him with a maximum margin of error of 5 percentage points.
What information do we need? Sampling strategy and sampling frame Simple Random Sample from the list of eligible voters Formula for the sample size ? =?2? 1 ? ? ??= 1 +? ?2 ? Margin of error and confidence interval Margin of error of 5 percent and the 95% confidence interval Estimate of the prevalence Unknown so will use the worst case scenario of 50% Total number of voters Known to be 10,000 from the information in the sampling frame
Calculations for an infinite population ? =?2? 1 ? ?2 confidence level = 95% prevalence = 50 percent margin of error = 5 percent t = 1.96 P = 0.5 E = 0.05 ? =1.9620.5 1 0.5 384 0.052
Applying finite population correction ? ??= 1 +? ? n = 384 N = 10,000 384 ??= 370 384 10,000 1 +
confidence level: 95% For an infinite population Prevalen ce 10% 20% 30% 40% 50% t=1.96 margin of error 1% 2% 864 1,537 2,017 2,305 2,401 3% 384 683 896 1,024 1,067 5% 138 246 323 369 384 10% 35 61 81 92 96 3,457 6,146 8,067 9,220 9,604 N=10,00 0 Prevalen ce margin of error 1% 2% 796 1,332 1,678 1,873 1,936 3% 370 639 823 929 964 5% 136 240 313 356 370 10% 34 61 80 91 95 10% 20% 30% 40% 50% 2,569 3,807 4,465 4,797 4,899
