## Confidence Interval for Proportions Exercise

1. Samples of size, n are taken from populations with a probabilty of success of π.

Use the values of n and p, the sample size and proportion, given below, to find confidence intervals for the population proportion with the levels of confidence indicated.

 n p Confidence level a 60 0.54 99% b 200 0.4 90% c 1000 0.45 86%

2. A political candidate finds that in a random sample of 300 constituents, 34% support her party. Find the 95% confidence interval for the support she in fact has.

3. Houses on a street are numbered from 1 to 627. Roimata takes a random sample of 40 houses.

She finds that in 25 of them, there are more than 3 residents.

Find a 90% confidence interval for the proportion of all houses in the street having more than three residents.

4. A toy manufacturer wants to test for the proportion of faulty toys in a large batch produced by a particular factory. He tests a random sample of 200 toys and finds that 25 are faulty.

Calculate a 94% confidence interval for the proportion of faulty toys in the complete batch.

5. In a survey carried out in London, 38 people out of a random sample of 70 people said that they bought the Daily Mirror regularly. Find a 99% confidence interval for the proportion of people who buy the Daily Mirror in London.