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.
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?