Margin of Error worksheet

1. Margin of error: 3.97%

1. Look up the z* value for 99% confidence. It sets how wide the range must be to be that sure

   $\mathrm{z*}$$=2.5758$

2. Find the standard error, how much a poll result typically wobbles from sample to sample. Use p as a decimal and n as the sample size

   $\mathrm{SE}$$=\sqrt{\frac{0.5\times \left(1-0.5\right)}{\mathrm{1,050}}}$$=0.01543$

3. Multiply z* by the standard error to get the margin of error E

   $E$$=2.5758\times 0.01543$$=0.039746$

4. Multiply by 100 to read the margin in percentage points

   $0.039746\times 100$$=\mathrm{3.974591\%}$

2. Margin of error: 2.15%

1. Look up the z* value for 78% confidence. It sets how wide the range must be to be that sure

   $\mathrm{z*}$$=1.2265$

2. Find the standard error, how much a poll result typically wobbles from sample to sample. Use p as a decimal and n as the sample size

   $\mathrm{SE}$$=\sqrt{\frac{0.44\times \left(1-0.44\right)}{800}}$$=0.01755$

3. Multiply z* by the standard error to get the margin of error E

   $E$$=1.2265\times 0.01755$$=0.021525$

4. Multiply by 100 to read the margin in percentage points

   $0.021525\times 100$$=\mathrm{2.152548\%}$

3. Margin of error: 2.58%

1. Look up the z* value for 90% confidence. It sets how wide the range must be to be that sure

   $\mathrm{z*}$$=1.6449$

2. Find the standard error, how much a poll result typically wobbles from sample to sample. Use p as a decimal and n as the sample size

   $\mathrm{SE}$$=\sqrt{\frac{0.56\times \left(1-0.56\right)}{\mathrm{1,000}}}$$=0.015697$

3. Multiply z* by the standard error to get the margin of error E

   $E$$=1.6449\times 0.015697$$=0.025819$

4. Multiply by 100 to read the margin in percentage points

   $0.025819\times 100$$=\mathrm{2.581949\%}$

4. Margin of error: 2.69%

1. Look up the z* value for 90% confidence. It sets how wide the range must be to be that sure

   $\mathrm{z*}$$=1.6449$

2. Find the standard error, how much a poll result typically wobbles from sample to sample. Use p as a decimal and n as the sample size

   $\mathrm{SE}$$=\sqrt{\frac{0.6\times \left(1-0.6\right)}{900}}$$=0.01633$

3. Multiply z* by the standard error to get the margin of error E

   $E$$=1.6449\times 0.01633$$=0.02686$

4. Multiply by 100 to read the margin in percentage points

   $0.02686\times 100$$=\mathrm{2.686035\%}$

5. Margin of error: 3.82%

1. Look up the z* value for 95% confidence. It sets how wide the range must be to be that sure

   $\mathrm{z*}$$=1.96$

2. Find the standard error, how much a poll result typically wobbles from sample to sample. Use p as a decimal and n as the sample size

   $\mathrm{SE}$$=\sqrt{\frac{0.45\times \left(1-0.45\right)}{650}}$$=0.019513$

3. Multiply z* by the standard error to get the margin of error E

   $E$$=1.96\times 0.019513$$=0.038245$

4. Multiply by 100 to read the margin in percentage points

   $0.038245\times 100$$=\mathrm{3.824538\%}$

6. Margin of error: 1.42%

1. Look up the z* value for 68% confidence. It sets how wide the range must be to be that sure

   $\mathrm{z*}$$=0.9945$

2. Find the standard error, how much a poll result typically wobbles from sample to sample. Use p as a decimal and n as the sample size

   $\mathrm{SE}$$=\sqrt{\frac{0.58\times \left(1-0.58\right)}{\mathrm{1,200}}}$$=0.014248$

3. Multiply z* by the standard error to get the margin of error E

   $E$$=0.9945\times 0.014248$$=0.014169$

4. Multiply by 100 to read the margin in percentage points

   $0.014169\times 100$$=\mathrm{1.416884\%}$

7. Margin of error: 1.17%

1. Look up the z* value for 58% confidence. It sets how wide the range must be to be that sure

   $\mathrm{z*}$$=0.8064$

2. Find the standard error, how much a poll result typically wobbles from sample to sample. Use p as a decimal and n as the sample size

   $\mathrm{SE}$$=\sqrt{\frac{0.64\times \left(1-0.64\right)}{\mathrm{1,100}}}$$=0.014473$

3. Multiply z* by the standard error to get the margin of error E

   $E$$=0.8064\times 0.014473$$=0.011671$

4. Multiply by 100 to read the margin in percentage points

   $0.011671\times 100$$=\mathrm{1.167097\%}$

8. Margin of error: 2.85%

1. Look up the z* value for 95% confidence. It sets how wide the range must be to be that sure

   $\mathrm{z*}$$=1.96$

2. Find the standard error, how much a poll result typically wobbles from sample to sample. Use p as a decimal and n as the sample size

   $\mathrm{SE}$$=\sqrt{\frac{0.54\times \left(1-0.54\right)}{\mathrm{1,175}}}$$=0.01454$

3. Multiply z* by the standard error to get the margin of error E

   $E$$=1.96\times 0.01454$$=0.028497$

4. Multiply by 100 to read the margin in percentage points

   $0.028497\times 100$$=\mathrm{2.849738\%}$

9. Margin of error: 3.39%

1. Look up the z* value for 95% confidence. It sets how wide the range must be to be that sure

   $\mathrm{z*}$$=1.96$

2. Find the standard error, how much a poll result typically wobbles from sample to sample. Use p as a decimal and n as the sample size

   $\mathrm{SE}$$=\sqrt{\frac{0.45\times \left(1-0.45\right)}{825}}$$=0.017321$

3. Multiply z* by the standard error to get the margin of error E

   $E$$=1.96\times 0.017321$$=0.033948$

4. Multiply by 100 to read the margin in percentage points

   $0.033948\times 100$$=\mathrm{3.394757\%}$

10. Margin of error: 2.74%

1. Look up the z* value for 90% confidence. It sets how wide the range must be to be that sure

   $\mathrm{z*}$$=1.6449$

2. Find the standard error, how much a poll result typically wobbles from sample to sample. Use p as a decimal and n as the sample size

   $\mathrm{SE}$$=\sqrt{\frac{0.52\times \left(1-0.52\right)}{900}}$$=0.016653$

3. Multiply z* by the standard error to get the margin of error E

   $E$$=1.6449\times 0.016653$$=0.027392$

4. Multiply by 100 to read the margin in percentage points

   $0.027392\times 100$$=\mathrm{2.739229\%}$