Question

a)

BHMT protein Blood samples from 268 ferrets (above left) will be used to determine the concentration of liver 2 25 enzyme in blood, an indicator of dietary stress. You are asked to summarize the findings by calculating the confidence intervals of both the mean and the variance in BHMT concentrations. Which sampling distributions (of the ones shown) above would you use and why? Mean in the middle because the sampling distribution closely resembles the data, variance on the right because variance is symmetrical Mean in the middle because the sampling distribution is symmetrical, variance on the right because variance is positive Mean on the right because the sampling distribution is symmetrical, variance in the middle because variance is always positive Mean on the right because the sampling distribution closely resembles the data, variance in the middle because variance is always positive Mean on the right because the sampling distribution closely resembles the data, variance cannot be calculated because it does not have a sampling distribution protein 50 40 30 20 10 DNA 50 40 30 20 10 0.00 0.05 0.10 0.15 FST What would be a good justification for using a non-parametric test to analyze differences in the data shown above? The samples are not normally distributed, but the variances follow a normal distribution The samples are normally distributed, but the variances are different The samples are not normally distributed, and are not random There isn't, a parametric test would do just as well O The samples are not normally distributed

Answer 1

Solution

a)

First point to note is that we are talking about the sampling distribution of the sample mean and sample variance and NOT about the distribution of the given set of data, which of course resembles the middle graph.

Since the sample size of 268 is large enough for Central Limit Theorem to be valid, sample mean has a normal distribution which is characterized by the symmetric property as in the right graph and hence the sampling distribution of the sample variance is a Chi-square distribution which is characterized by high negative skew as in middle graph. And, of course variance cannot be negative [variance is positive is not strictly a correct statement since it can be zero as well when all values are identical]. Thus, the correct answer is: Third Option Answer 1

b)

As a general rule, one takes recourse to non-parametric tests when the distribution of the base data is not known, or to be more specific, not Normal. Hence, the correct answer is: Last Option Answer 2

DONE