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