# 10.04 Confidence intervals for sample proportions

## Interactive practice questions

Given a sample size of $530$530 and a sample proportion of $40%$40%, find the approximate two-sided $95%$95% confidence interval for the population proportion using the given table.

Give your answer in the form $\left(a,b\right)$(a,b), and round your answer to two decimal places.

Easy
Less than a minute

To assist with road and transport planning, the council wants to estimate the proportion of people who use public transport to commute to work in the city.

They asked a sample of $500$500 people who work in the city if they use public transport to commute to work and $72.5%$72.5% of them responded that they did.

Ten samples, each of size $150$150, have their two-sided $90%$90% confidence interval calculated. How many of these samples would we expect to contain the true population proportion?

One hundred samples, each of size $300$300, have their two-sided $95%$95% confidence interval calculated. How many of these samples would we expect to contain the true population proportion?

### Outcomes

#### 4.5.3.1

understand the concept of an interval estimate for a parameter associated with a random variable

#### 4.5.3.2

use the approximate confidence interval [ ˆp-√(ˆp(1−ˆp)/n, ˆp+z√(ˆp(1−ˆp)/n), as an interval estimate for p, where z is the appropriate quantile for the standard normal distribution

#### 4.5.3.3

define the approximate margin of error E=z√(ˆp (1−ˆp)/n and understand the trade-off between margin of error and level of confidence