The concentration of a specific mineral in soil samples across an ancient site is normally distributed with a standard deviation of 15 mg/kg. An archaeological survey at Site Alpha involved 25 random samples, which yielded a mean mineral concentration of 84.0 mg/kg.
Determine a 98% confidence interval for the mean mineral concentration at Site Alpha.
A separate independent survey of 64 samples at Site Beta showed a mean mineral concentration of 90.5 mg/kg. A researcher suspects that the mean concentration at Site Beta is significantly higher than at Site Alpha.
Using a 5% level of significance and stating your hypotheses clearly, test whether the researcher's suspicion is supported by the data.
The regional baseline concentration for this mineral is denoted by μ\muμ. When the samples from Site Alpha and Site Beta are analysed independently at a 1% significance level, it is found that there is insufficient evidence to suggest the mean concentration of Site Alpha is less than μ\muμ, and insufficient evidence to suggest the mean concentration of Site Beta is less than μ\muμ.
Find the largest possible value for the baseline concentration μ\muμ.