2.05b Hypothesis test for binomial proportion

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SPS SPS FM Statistics 2025 April Q1
8 marks Moderate -0.3
It is known that, under standard conditions, 12% of light bulbs from a certain manufacturer have a defect. A quality improvement process has been implemented, and a random sample of 200 light bulbs produced after the improvements was selected. It was found that 15 of the 200 light bulbs were defective.
  1. State one assumption needed in order to use a binomial model for the number of defective light bulbs in the sample. [1]
  2. Test, at the 5% significance level, whether the proportion of defective light bulbs has decreased under the new process. [7]
SPS SPS SM Statistics 2024 September Q6
11 marks Standard +0.3
A television company believes that the proportion of households that can receive Channel C is 0.35.
  1. In a random sample of 14 households it is found that 2 can receive Channel C. Test, at the 2.5\% significance level, whether there is evidence that the proportion of households that can receive Channel C is less than 0.35. [7]
  2. On another occasion the test is carried out again, with the same hypotheses and significance level as in part (i), but using a new sample, of size \(n\). It is found that no members of the sample can receive Channel C. Find the largest value of \(n\) for which the null hypothesis is not rejected. Show all relevant working. [4]
OCR H240/02 2018 December Q9
7 marks Standard +0.3
Research has shown that drug A is effective in 32% of patients with a certain disease. In a trial, drug B is given to a random sample of 1000 patients with the disease, and it is found that the drug is effective in 290 of these patients. Test at the 2.5% significance level whether there is evidence that drug B is effective in a lower proportion of patients than drug A. [7]
OCR H240/02 2017 Specimen Q12
5 marks Challenging +1.2
The table shows information for England and Wales, taken from the UK 2011 census.
Total populationNumber of children aged 5-17
56 075 9128 473 617
A random sample of 10 000 people in another country was chosen in 2011, and the number, \(m\), of children aged 5-17 was noted. It was found that there was evidence at the 2.5% level that the proportion of children aged 5-17 in the same year was higher than in the UK. Unfortunately, when the results were recorded the value of \(m\) was omitted. Use an appropriate normal distribution to find an estimate of the smallest possible value of \(m\). [5]