Type I / Type II error interpretation

A question is this type if and only if, following a chi-squared test, the student is asked to identify or explain a Type I or Type II error in the context of the specific investigation.

2 questions · Standard +0.0

5.06a Chi-squared: contingency tables
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AQA S2 2008 January Q6
11 marks Moderate -0.3
6 A survey is carried out in an attempt to determine whether the salary achieved by the age of 30 is associated with having had a university education. The results of this survey are given in the table.
Salary < £30000Salary \(\boldsymbol { \geq }\) £30000Total
University education5278130
No university education6357120
Total115135250
  1. Use a \(\chi ^ { 2 }\) test, at the \(10 \%\) level of significance, to determine whether the salary achieved by the age of 30 is associated with having had a university education.
  2. What do you understand by a Type I error in this context?
AQA S2 2013 June Q2
10 marks Standard +0.3
2 A town council wanted residents to apply for grants that were available for home insulation. In a trial, a random sample of 200 residents was encouraged, either in a letter or by a phone call, to apply for the grants. The outcomes are shown in the table.
Applied for grantDid not apply for grantTotal
Letter30130160
Phone call142640
Total44156200
  1. The council believed that a phone call was more effective than a letter in encouraging people to apply for a grant. Use a \(\chi ^ { 2 }\)-test to investigate this belief at the \(5 \%\) significance level.
  2. After the trial, all the residents in the town were encouraged, either in a letter or by a phone call, to apply for the grants. It was found that there was no association between the method of encouragement and the outcome. State, with a reason, whether a Type I error, a Type II error or neither occurred in carrying out the test in part (a).
    (2 marks)