The height of a certain species of sunflower, in cm, is normally distributed with a mean of 180 cm and a standard deviation of 12 cm. A gardener has one of these sunflowers.
Find the probability that the sunflower is taller than 170 cm.
A sunflower is already 170 cm tall. Find the probability that it grows to be taller than 195 cm.
The gardener believes that the mean height of these sunflowers is greater than 180 cm. He took a random sample of 36 sunflowers and found that their mean height was 183.5 cm. Stating your hypotheses clearly and using a 5% level of significance, test the gardener's 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.