Question

Decide whether each of the following statements is either true or false. You MUST explain your reasoning.

(a) If in a population, the shortest person is 1.5 metres tall and the tallest person is 2 metres tall, then the average height is always closer to 1.75 metres than to 2 metres.

(b) If the correlation between two variables X and Y is positive, then Y is small (below the average Y value) whenever X is small (below the average X value).

(c) I have collected information on the ethnic origins and annual salaries of all University of Regina faculty members. A good way to display the relationship between ethnic origin and annual salaries is with a scatterplot.

(d) Suppose that I take a simple random sample of University of Regina students and construct a 95% confidence interval for the mean IQ of all U of R students. My confidence interval is 110 ± 3. Now I want to use the same data to conduct a level α = 0.01 significance test of H0: the mean IQ of all U of R students is 112, against the alternative Ha: the mean IQ of all U of R students is not 112. Based on the confidence interval, I would reject H0.

Answer 1