The time taken for James to commute to work, in minutes, is normally distributed with a mean of 35 minutes and a standard deviation of 4 minutes. On a particular morning, James starts his commute.
Find the probability that the commute takes longer than 32 minutes.
James has already been commuting for 32 minutes. Find the probability that his commute lasts for another 8 minutes.
James believes that the mean commute time is longer than 35 minutes. He records a random sample of 16 commutes and finds that their mean time is 36.8 minutes. Stating your hypotheses clearly and using a 5% level of significance, test James' belief.
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.