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.