Sample Size worksheet

1. Required sample size: 15 measurements

1. Look up the z value (z*) for 90% confidence. The surer you want to be, the bigger it gets, and the more responses you need

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

2. For an average, multiply z* by the spread (σ), divide by your margin (E), then square it

   $\mathrm{n₀}$$={\left(\frac{1.6449\times 16}{7}\right)}^2$$=14.135084$

3. Round up to the next whole number, because rounding down would miss your margin

   $\text{round up}$$=15$

2. Required sample size: 577 responses

1. Look up the z value (z*) for 95% confidence. The surer you want to be, the bigger it gets, and the more responses you need

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

2. For a percentage, use your expected share (p) and margin (E) as decimals. Square z*, times p × (1 − p), then divide by E squared

   $\mathrm{n₀}$$=\frac{{1.96}^2\times 0.4\times \left(1-0.4\right)}{{0.04}^2}$$=576.218823$

3. Round up to the next whole number, because rounding down would miss your margin

   $\text{round up}$$=577$

3. Required sample size: 419 responses

1. Look up the z value (z*) for 90% confidence. The surer you want to be, the bigger it gets, and the more responses you need

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

2. For a percentage, use your expected share (p) and margin (E) as decimals. Square z*, times p × (1 − p), then divide by E squared

   $\mathrm{n₀}$$=\frac{{1.6449}^2\times 0.45\times \left(1-0.45\right)}{{0.04}^2}$$=418.513753$

3. Round up to the next whole number, because rounding down would miss your margin

   $\text{round up}$$=419$

4. Required sample size: 13 measurements

1. Look up the z value (z*) for 90% confidence. The surer you want to be, the bigger it gets, and the more responses you need

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

2. For an average, multiply z* by the spread (σ), divide by your margin (E), then square it

   $\mathrm{n₀}$$={\left(\frac{1.6449\times 13}{6}\right)}^2$$=12.701023$

3. Round up to the next whole number, because rounding down would miss your margin

   $\text{round up}$$=13$

5. Required sample size: 260 responses

1. Look up the z value (z*) for 90% confidence. The surer you want to be, the bigger it gets, and the more responses you need

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

2. For a percentage, use your expected share (p) and margin (E) as decimals. Square z*, times p × (1 − p), then divide by E squared

   $\mathrm{n₀}$$=\frac{{1.6449}^2\times 0.4\times \left(1-0.4\right)}{{0.05}^2}$$=259.732172$

3. Round up to the next whole number, because rounding down would miss your margin

   $\text{round up}$$=260$

6. Required sample size: 258 responses

1. Look up the z value (z*) for 92% confidence. The surer you want to be, the bigger it gets, and the more responses you need

   $\mathrm{z*}$$=1.7507$

2. For a percentage, use your expected share (p) and margin (E) as decimals. Square z*, times p × (1 − p), then divide by E squared

   $\mathrm{n₀}$$=\frac{{1.7507}^2\times 0.7\times \left(1-0.7\right)}{{0.05}^2}$$=257.451744$

3. Round up to the next whole number, because rounding down would miss your margin

   $\text{round up}$$=258$

7. Required sample size: 23 measurements

1. Look up the z value (z*) for 95% confidence. The surer you want to be, the bigger it gets, and the more responses you need

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

2. For an average, multiply z* by the spread (σ), divide by your margin (E), then square it

   $\mathrm{n₀}$$={\left(\frac{1.96\times 17}{7}\right)}^2$$=22.656767$

3. Round up to the next whole number, because rounding down would miss your margin

   $\text{round up}$$=23$

8. Required sample size: 44 measurements

1. Look up the z value (z*) for 90% confidence. The surer you want to be, the bigger it gets, and the more responses you need

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

2. For an average, multiply z* by the spread (σ), divide by your margin (E), then square it

   $\mathrm{n₀}$$={\left(\frac{1.6449\times 16}{4}\right)}^2$$=43.288695$

3. Round up to the next whole number, because rounding down would miss your margin

   $\text{round up}$$=44$

9. Required sample size: 7 measurements

1. Look up the z value (z*) for 56% confidence. The surer you want to be, the bigger it gets, and the more responses you need

   $\mathrm{z*}$$=0.7722$

2. For an average, multiply z* by the spread (σ), divide by your margin (E), then square it

   $\mathrm{n₀}$$={\left(\frac{0.7722\times 13}{4}\right)}^2$$=6.298232$

3. Round up to the next whole number, because rounding down would miss your margin

   $\text{round up}$$=7$

10. Required sample size: 657 responses

1. Look up the z value (z*) for 99% confidence. The surer you want to be, the bigger it gets, and the more responses you need

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

2. For a percentage, use your expected share (p) and margin (E) as decimals. Square z*, times p × (1 − p), then divide by E squared

   $\mathrm{n₀}$$=\frac{{2.5758}^2\times 0.45\times \left(1-0.45\right)}{{0.05}^2}$$=656.854764$

3. Round up to the next whole number, because rounding down would miss your margin

   $\text{round up}$$=657$