AQA S3 2010 June — Question 6

Exam BoardAQA
ModuleS3 (Statistics 3)
Year2010
SessionJune
TopicHypothesis test of a normal distribution
6
  1. A district council claimed that more than 80 per cent of the complaints that it received about the delivery of its services were answered to the satisfaction of complainants before reaching formal status. An analysis of a random sample of 175 complaints revealed that 28 reached formal status.
    1. Construct an approximate \(95 \%\) confidence interval for the proportion of complaints that reach formal status.
    2. Hence comment on the council's claim.
  2. The district council also claimed that less than 40 per cent of all formal complaints were due to a failing in the delivery of its services. An analysis of the 50 formal complaints received during 2007/08 showed that 16 were due to a failing in the delivery of its services.
    1. Using an exact test, investigate the council's claim at the \(10 \%\) level of significance. The 50 formal complaints received during 2007/08 may be assumed to be a random sample.
    2. Determine the critical value for your test in part (b)(i).
    3. In fact, only 25 per cent of all formal complaints were due to a failing in the delivery of the council's services. Determine the probability of a Type II error for a test of the council's claim at the \(10 \%\) level of significance and based on the analysis of a random sample of 50 formal complaints.
      (4 marks)
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