## evaluate the null hypothesis that different hair colors have equal probabilities.

In R-Commander, click Data → Data in pacakges → Read data set from an attached package, then select the HairEyeColor data from the datasets package. The data include hair and eye color and sex for 592 statistics students at the University of Delaware reported by Snee (1974). The first column shows different hair colors (Black, Brown, Red, Blond), the second column shows different eye colors (Brown, Blue, Hazel, Green), and the third column shows genders (Male, Female) of students. For each row, the last column shows the number of students with a specific hair color, eye color, and gender.

(a) Use Pearson’s χ 2 test to evaluate the null hypothesis that different hair colors have equal probabilities. Use Pearson’s χ 2 test to evaluate the null hypothesis that different eye colors have equal probabilities.

(b) Create a 4×4 contingency table where the rows represent different hair colors and the columns represent different eye colors. Is there a relationship between hair color and eye color?

(c) Enter the contingency table in R-Commander and use Chi-square test of independence to evaluate the relationship between hair color and eye color.

### Determine the outlet concentration x1 in the water solution and in the trichloroethane solution using an analytical equation.

Predicting Extraction for an Existing Tower with a Given Number of Steps. An existing tower contains 5.0 theoretical steps. It is desired to predict its performance under the following conditions….

### Calculate the minimum solvent that can be used. [Hint: In this case, the tie line through the feed L0 represents the condition for minimum solvent flow rate.

Minimum Solvent and Countercurrent Extraction of Acetone. An aqueous feed solution of 1000 kg/h containing 23.5 wt % acetone and 76.5 wt % water is being extracted in a countercurrent….

### Determine the break-point time, the fraction of total capacity used up to the break point, the length of the unused bed, and the saturation loading capacity of the solid.

Drying of Nitrogen and Scale-Up of a Column. Using molecular sieves, water vapor was removed from nitrogen gas in a packed bed (C1) at 28.3°C. The column height was 0.268….