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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.