A gambler thinks that a coin is fair and is equally likely to turn up heads or tails when the coin is flipped. Which of the following tests should the gambler use to fest this hypothesis?

A t-test is used to compare the means of two groups and is not appropriate for comparing observed versus expected counts of categorical outcomes.

The Chi-squared test (specifically, a chi-squared goodness-of-fit test) is used to determine if there is a significant difference between the observed frequencies and the expected frequencies in one or more categories. In this scenario, the observed frequencies would be the counts of heads and tails, and the expected frequencies would be equal counts if the coin were fair, making it ideal for testing this hypothesis about categorical outcomes.

A rank sum test (like the Mann-Whitney U test) is a non-parametric test used to compare distributions of two independent samples, which is not suitable for a single categorical outcome comparison.

A ratio test is typically used in calculus to determine the convergence of an infinite series, not a statistical hypothesis test for coin fairness.