Chapter 7.4, Problem 28E

To determine

To determine whether there is an association between gender and type of degree students are planning to do.

Answer to Problem 28E

Yes, there is an association between gender and type of degree

This means more number of females are planning to do associate’s degree and master’s degree as compared to males.

Also more number of males are planning to Bachelor’s as compared to females.

Explanation of Solution

Given information:

Two-way table given below:

  

Concept used:

Use conditional relative frequency to determine association between gender and type of degree

Total $=58+126+42+62+118+48=454$

	Associate’s	Bachelor’s	Master’s
Male	$\frac{58}{454}\approx 0.13$	$\frac{126}{454}\approx 0.28$	$\frac{42}{454}\approx 0.09$
Female	$\frac{62}{454}\approx 0.14$	$\frac{118}{454}\approx 0.26$	$\frac{48}{454}\approx 0.11$
Total	0.27	0.54	0.20

	Associate’s	Bachelor’s	Master’s
Male	$\frac{0.13}{0.27}=0.48$	$\frac{0.28}{0.54}\approx 0.52$	$\frac{0.09}{0.20}=0.45$
Female	$\frac{0.14}{0.27}=0.52$	$\frac{0.26}{0.54}=0.48$	$\frac{0.11}{0.20}=0.55$

Yes, there is an association between gender and type of degree

Of the students $52\%$ of females have planned to do associate’s degree while $48\%$ of males have associate’s degree.

Of the students $52\%$ of males have planned to do bachelor’s degree while $48\%$ of females have planned to do bachelor’s degree.

Of the students $45\%$ of males have planned to do master’s degree while $55\%$ of females have planned to do master’s degree.

This means more number of females are planning to do associate’s degree and master’s degree as compared to males.

Also more number of males are planning to Bachelor’s as compared to females.