According to Forbes, there are currently 2,153 billionaires in the US. A professor studying wealth in the US claims that billionaires are, on average, 10 years older than millionaires in the US. To investigate this belief, he selects a random sample of 10 billionaires in the US and 10 millionaires in the US and records the ages of each of these individuals. Here are dotplots and summary statistics of the data. Do these data provide convincing evidence that the average age of billionaires in the US is more than 10
years greater than the average age of millionaires?
a) What are the appropriate hypotheses for this test of significance?
b) Are the conditions for inference met? Justify your answer.
c) The researcher determines that the null hypothesis cannot be rejected using a significance level
of 0.05. What standardized test statistic and P-value lead to this decision? Draw and shade an
appropriate distribution to illustrate your answer.