New Zealand
Level 8 - NCEA Level 3

# Margins of error

## Interactive practice questions

Using the table provided, calculate the margin of error for a $90%$90% confidence interval for a sample of size $140$140 that has a sample proportion of $0.63$0.63. Give your answer to two decimal places.

Standard Normal Probability z-value
$0.9$0.9 $1.282$1.282
$0.925$0.925 $1.440$1.440
$0.95$0.95 $1.645$1.645
$0.975$0.975 $1.960$1.960
$0.99$0.99 $2.326$2.326
$0.995$0.995 $2.576$2.576
Easy
Approx 4 minutes

Using the table provided, calculate the margin of error for an $80%$80% confidence interval for a sample of size $160$160 that has a sample proportion of $0.56$0.56. Give your answer to two decimal places.

Using the table provided, calculate the margin of error for a $95%$95% confidence interval for a sample of size $110$110 that has a sample proportion of $0.54$0.54. Give your answer to two decimal places.

Using the table provided, calculate the margin of error for a $99%$99% confidence interval for a sample of size $170$170 that has a sample proportion of $0.4$0.4. Give your answer to two decimal places.

### Outcomes

#### S8-2

Make inferences from surveys and experiments: A determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem B using methods such as resampling or randomisation to assess

#### S8-3

Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies: A critiquing causalrelationship claims B interpreting margins of error.

#### 91582

Use statistical methods to make a formal inference

#### 91584

Evaluate statistically based reports