HairEyeColor is a ready-to-use data set in R that you haven’t yet come across. This 4 × 4 × 2 array provides frequencies of hair and eye colors of 592 statistics students, split by sex (Snee, 1974).
a. Perform and interpret, at a significance level of α = 0.01, a chisquared test of independence for hair against eye color for all students, regardless of their sex.
In Exercise 8.1 on page 161, you accessed the Duncan data set of the contributed package car, which contains markers of job prestige collected in 1950. Install the package if you haven’t already and load the data frame.
b. The first column of Duncan is the variable type, recording the type of job as a factor with three levels: prof (professional or managerial), bc (blue collar), and wc (white collar). Construct appropriate hypotheses and perform a chi-squared GOF test to determine whether the three job types are equally represented in the data set.
i. Interpret the resulting p-value with respect to a significance level of α = 0.05.
ii. What conclusion would you reach if you used a significance level of α = 0.01?