Find critical region

A question is this type if and only if it asks to determine the critical region for a hypothesis test at a given significance level, without carrying out the test.

2 questions · Standard +0.3

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Edexcel S2 2022 January Q3
9 marks Standard +0.3
3 A photocopier in a school is known to break down at random at a mean rate of 8 times per week.
  1. Give a reason why a Poisson distribution could be used to model the number of breakdowns. The headteacher of the school replaces the photocopier with a refurbished one and wants to find out if the rate of breakdowns has increased or decreased.
  2. Write down suitable null and alternative hypotheses that the headteacher should use. The refurbished photocopier was monitored for the first week after it was installed.
  3. Using a \(5 \%\) level of significance, find the critical region to test whether the rate of breakdowns has now changed.
  4. Find the actual significance level of a test based on the critical region from part (c). During the first week after it was installed there were 4 breakdowns.
  5. Comment on this finding in the light of the critical region found in part (c).
Edexcel S2 Q1
3 marks Standard +0.3
\begin{enumerate} \item A company that makes ropes for mountaineering wants to assess the breaking strain of its ropes.
  1. Explain why a sample survey, and not a census, should be used.
  2. Suggest an appropriate sampling frame. \item It is thought that a random variable \(X\) has a Poisson distribution whose mean, \(\lambda\), is equal to 8 . Find the critical region to test the hypothesis \(\mathrm { H } _ { 0 } : \lambda = 8\) against the hypothesis \(\mathrm { H } _ { 1 } : \lambda < 8\), working at the \(1 \%\) significance level. \item A child cuts a 30 cm piece of string into two parts, cutting at a random point.