for the following questions state the:

correct statement of null and alternate hypotheses;

correct critical values from the table NOT a calculator or other program;

correct calculation of test statistics;

the correct conclusion in the form of a statement about the null hypothesis;

and an analysis of results, where requested

1. Heights of Presidents and Runners-Up

Theories have been developed about the heights of winning candidates for the U.S. presidency and the heights of candidates who were runners-up. Listed below are heights (in inches) from recent presidential elections. Is there a linear correlation between the heights of candidates who won and the heights of the candidates who were runners-up?

Winner 69.5 73 73 74 74.5 74.5 71 71

Runner-ups 72 69.5 70 68 74 74 73 76

2. Crickets and Temperature

One classic application of correlation involves the association between temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 min and the corresponding temperatures in Fahrenheit (based on data from The Song of Insects by George W. Pierce, Harvard University Press. Is there a linear correlation between the number of chirps in 1 min and the temperature?

Chirps in 1 min 882 1188 1104 864 1200 1032 960 900

Temperature (F) 69.7 93.3 84.3 76.3 88.6 82.6 71.6 79.6