Calculate CI for proportion

Given a sample size and number of successes, calculate an approximate confidence interval for a population proportion p.

28 questions · Moderate -0.3

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WJEC Further Unit 5 2024 June Q3
7 marks Moderate -0.8
Tony runs a pie stand that sells two types of pie outside a football ground. He wants to estimate the probability that a customer will buy a steak pie rather than a vegetable pie. He conducts a survey by randomly selecting customers and recording their choice of pie. When he feels he has enough data, he notes that 55 customers bought steak pies and 25 bought vegetable pies.
  1. Calculate an approximate 90\% confidence interval for \(p\), the probability that a randomly selected customer buys a steak pie. [6]
  2. Suppose that Tony carries out 50 such surveys and calculates 90\% confidence intervals for each survey. Determine the expected number of these confidence intervals that would contain the true value of \(p\). [1]
WJEC Further Unit 5 Specimen Q4
12 marks Standard +0.3
  1. In an opinion poll of 1800 people, 1242 said that they preferred red wine to white wine. Calculate a 95% confidence interval for the proportion of people in the population who prefer red wine to white wine. [6]
  2. In another opinion poll of 1000 people on the same subject, the following confidence interval was calculated. \([0.672, 0.732]\). Determine
    1. the number of people in the sample who stated that they prefer red wine to white wine,
    2. the confidence level of the confidence interval, giving your answer as a percentage correct to three significant figures. [6]
Pre-U Pre-U 9795/2 2014 June Q3
8 marks Standard +0.8
A random sample of 400 seabirds is taken from a colony, ringed, and returned, unharmed, to the colony. After a suitable period of time has elapsed, a second random sample of 400 seabirds is taken, and 20 of this second sample are found to be ringed. You may assume that the probability that a seabird is captured is independent of whether or not it has been ringed and that the colony remains unchanged at the time of the second sampling.
  1. Estimate the number of seabirds in the colony. [1]
  2. Find a 98% confidence interval for the proportion of seabirds in the colony which are ringed. [5]
  3. Deduce a 98% confidence interval for the number of seabirds in the colony. [2]