Conduct a chi-square test to determine if there is a significant difference between what was observed and what was expected.
a. State the null and alternative hypotheses in words.
b. Calculate the chi-square statistic using Equation (6.3).
c. In goodness-of-fit tests such as this, where all parameters are well defined, the degrees of freedom is equal to the number of cells minus 1. In this example, if we know how many 1s, 2s, 3s, 4s, and 5s were rolled, the number of 6s is fixed. Calculate the p-value for this study.
d. Are there enough observations to assume the chi- square distribution is appropriate?
e. Do you have evidence to believe your friend used an unfair die? Clearly state your conclusions.