At the beginning of a semester an anonymous survey was conducted on students in a statistics class. Two of the questions on the survey were about gender and whether or not students have equal, more, or less energy in the afternoon compared to the morning. Below are the results.

Equal Less More
Female 18 37 24
Male 9 15 23
What test should we perform to see if gender and energy level are associated?

a. Chi-square test of independence
b. Chi-square test of goodness of fit
c. Comparing two proportions
d. Comparing two means

a. Chi-square test of independence

Step-by-step explanation:

The chi square statistics is also used to test the hypothesis about the independence of two variables each of which is classified into a number of categories or attributes.

In the given problem the Equal , more or less are the attributes.

The goodness of fit test is applicable when the cell probabilities depend upon the unknown parameters  provided that the unknown parameters are replaced with their estimates and provided that one degree of freedom is deducted for each parameter estimated.

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y

19.side- angle- side

20. angle- side- angle

step-by-step explanation: