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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.