A teacher sees students straggling into her class at highly diverse times. She

Step 1
Introduction:
The lateness scores of the arriving students varied between 0 and 600; these scores are measured in seconds, and is the number of seconds that a student arrives late for class. The lateness score can be any value between 0 and 600, and the value 0 is absolute, implying that the person was not late. Thus, the lateness score is a continuous variable, measured on the ratio scale.
The exam average of a student over the semester can take any value between 0 and the maximum average marks in the exam, with the value 0, which implies that the person did not get any score on an average throughout the semester, being absolute. Thus, the lateness score is a continuous variable, measured on the ratio scale.
The teacher wants to estimate the degree of relationship between two continuous, ratio scale variable- the lateness and exam scores of the student.
Step 2
Explanation:
The z-test is used when one wishes to test if the true population mean of a single population equals a given constant value, when the population standard deviation is known. The one-sample t-test is used for the same purpose, but when the population standard deviation is unknown. But here, two different populations are to be compared.
Independent groups t-test is used when the means for the same or comparable variables for two independent populations are to be compared. Dependent groups t-test is used when the means for the same or comparable variables for two dependent populations are to be compared. But here, two completely different variables- lateness score (time) and exam scores are to be compared.
One factor ANOVA is used when three or more categories of a single factor are to be compared with respect to their means, provided the data are independent and normally distributed, the groups are independent, and the populations are homoscedastic (same variance). Two factor ANOVA is used when three or more categories of one factor, and three or more categories of a different factor are to be compared separately with respect to their means, provided the data satisfy similar conditions. However, two continuous, and not categorical variables are to be compared here.
The t-test for ${\displaystyle r>0}$ would be used if one wishes to test for the presence of significant positive correlation, r between two continuous variables. However, the teacher here wants to test the degree of relationship between the two variables, and not just positive linear relationship. Further, the teacher is likely to want to test if higher lateness is associated with lower exam scores on average, and not to test if higher lateness is associated with higher exam scores on average.
The chi-square test of association is useful for testing for the presence of association between two categorical variables. Although the two variables here are continuous, it is possible for the teacher to divide each of the lateness scores exam average scores into several classes or categories, and then use chi-square test of association to estimate the degree of relationship between the variables.
Phi coefficient is used to measure the association between two binary variables. However, each variable here is non-binary. Even if it is possible to classify each variable into exactly two categories, much information regarding the original data would be lost in such a process, which is not desirable.
Cramer’s phi is usually useful for measuring the association between two nominal or categorical variables. Although the variables here are ratio scale, like in case of chi-square test, it is possible for the teacher to divide each of the lateness scores exam average scores into several classes or categories, and then use Cramer’s phi to estimate the degree of relationship between the variables.
Point biserial correlation or point biserial r is a measure of association between a continuous, and a binary variable. However, both variables in this study are continuous.
The quantity eta-squared calculates the effect size of a test, by measuring the standardized difference of the sample mean from the population mean, or between two sample means of comparable quantities. However, the two means here are not directly comparable.
The quantity r, also called Pearson correlation coefficient is a measure of strength of linear association between any two continuous, ratio scale variables, provided some inherent conditions are satisfied. The quantity r-squared or ${\displaystyle r^2}$ is simply the square of r, which gives the proportion (or percentage, when multiplied with 100) of variation in the dependent variable that is being explained by the independent variable, when it is possible to determine one of the variables in the study to be dependent on the other one. Here, as both the variables are continuous, ratio scale variables, r or ${\displaystyle r^2}$ can be used to measure the degree of association between them, if the researcher is specifically interested in determining the degree of linear association, and if it is possible to determine one of the variables as dependent on the other. Logically speaking, exam score of a student might be considered to be dependent on the level of lateness to class, at least from the teacher’s point of view.
Thus, among the given tests, it would be the most suitable to use r-squared or r; additionally, with some modifications to the available data, chi-square test or Cramer’s phi might also be used.