The time taken for a computer script to complete a specific task is normally distributed with a mean of 40 seconds and a standard deviation of 6 seconds.
Find the probability of the script taking longer than 50 seconds.
A developer suspects that a recent update has changed the mean completion time.
Write down a null and alternative hypothesis for a two-tailed test.
A random sample of 9 scripts is run, resulting in a mean completion time of 45 seconds.
Test at the 1% significance level whether there is evidence that the mean completion time has changed.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.