Calculate Type I error probability

A question is this type if and only if it asks the student to find or calculate the probability of making a Type I error, given a specific test procedure or critical region.

27 questions · Standard +0.1

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WJEC Unit 2 2018 June Q04
9 marks Moderate -0.3
Edward can correctly identify 20% of types of wild flower. He studies some books to see if he can improve how often he can correctly identify types of wild flower. He collects a random sample of 10 types of wild flower in order to test whether or not he has improved.
    1. Write suitable hypotheses for this test.
    2. State a suitable test statistic that he could use. [2]
  2. Using a 5% level of significance, find the critical region for this test. [3]
  3. State the probability of a Type I error for this test and explain what it means in this context. [2]
  4. Edward correctly identifies 4 of the 10 types of wild flower he collected. What conclusion should Edward reach? [2]
SPS SPS SM Statistics 2024 January Q6
6 marks Standard +0.3
A firm claims that no more than 2\% of their packets of sugar are underweight. A market researcher believes that the actual proportion is greater than 2\%. In order to test the firm's claim, the researcher weighs a random sample of 600 packets and carries out a hypothesis test, at the 5\% significance level, using the null hypothesis \(p = 0.02\).
  1. Given that the researcher's null hypothesis is correct, determine the probability that the researcher will conclude that the firm's claim is incorrect. [5]
  2. The researcher finds that 18 out of the 600 packets are underweight. A colleague says "18 out of 600 is 3\%, so there is evidence that the actual proportion of underweight bags is greater than 2\%." Criticise this statement. [1]