Find actual significance level

A question is this type if and only if it asks to calculate the actual significance level (actual probability in tail(s)) after a critical region has been determined.

2 questions · Standard +0.3

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OCR S2 2007 June Q5
7 marks Standard +0.3
5 The number of system failures per month in a large network is a random variable with the distribution \(\operatorname { Po } ( \lambda )\). A significance test of the null hypothesis \(\mathrm { H } _ { 0 } : \lambda = 2.5\) is carried out by counting \(R\), the number of system failures in a period of 6 months. The result of the test is that \(\mathrm { H } _ { 0 }\) is rejected if \(R > 23\) but is not rejected if \(R \leqslant 23\).
  1. State the alternative hypothesis.
  2. Find the significance level of the test.
  3. Given that \(\mathrm { P } ( R > 23 ) < 0.1\), use tables to find the largest possible actual value of \(\lambda\). You should show the values of any relevant probabilities.
Edexcel S2 2014 January Q4
7 marks Standard +0.3
  1. The number of telephone calls per hour received by a business is a random variable with distribution \(\operatorname { Po } ( \lambda )\).
Charlotte records the number of calls, \(C\), received in 4 hours. A test of the null hypothesis \(\mathrm { H } _ { 0 } : \lambda = 1.5\) is carried out. \(\mathrm { H } _ { 0 }\) is rejected if \(C > 10\)
  1. Write down the alternative hypothesis.
  2. Find the significance level of the test. Given that \(\mathrm { P } ( C > 10 ) < 0.1\)
  3. find the largest possible value of \(\lambda\) that can be found by using the tables.