The height of sunflowers after 8 weeks is normally distributed with a standard deviation of 12 cm. A random sample of 36 sunflowers from Farm A had a mean height of 115.5 cm.
Calculate a 95% confidence interval for the mean height of sunflowers at Farm A.
An independent random sample of 40 sunflowers from Farm B had a mean height of 120.2 cm. A researcher claimed that the mean height of sunflowers from Farm B is greater than the mean height of sunflowers from Farm A.
Stating your hypotheses clearly, use a 10% significance level to test the researcher's claim.
The national average height for these sunflowers after 8 weeks is μ\muμ. Considering the two samples separately, at the 5% level of significance, there is insufficient evidence that the mean height for Farm A is less than μ\muμ, and insufficient evidence that the mean height for Farm B is less than μ\muμ.
Find the largest possible value for μ\muμ.
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.