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.

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution

Which of the following functions corresponds to the above sinusoid? a. 10 cos πx - 5 b. -5 sin x - 5 c. -10 cos πx/2 - 0.5 d. 10 sin πx - 5